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Creating scaling and reflection transformation matrices (which are diagonal)
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/linear-transformation-examples-rotations-in-r2?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
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The Kings and Generals animated historical documentary series on the ancient civilizations continues with a video on the evolution of the Indo-European Languages, as we give a summary of how this language family formed and how the languages belonging to each are still connected to each other:
Arabia Before Islam: Religion, Society, Culture: https://youtu.be/07OsSSt0ytc
Vandals: https://youtu.be/-IpbeEW6I9Y
How Rome Conquered Greece: https://youtu.be/v5q1rerf-qw
Did the Trojan War Really Happen: https://youtu.be/12eHJL2yRtk
Demosthenes: https://youtu.be/ABS1iepXG0U
Ancient Greek Politics and Diplomacy: https://youtu.be/MVnp4NilDLI
Pyrrhic Wars: https://youtu.be/2QBA6ZPmj3Q
Ancient Macedonia before Alexander the Great and Philip II: https://youtu.be/FXX1FVYysjQ
Diplomatic Genius of Philip of Macedon: https://youtu.be/yVTrkESkuTw
Etruscans: https://youtu.be/FkySjRwUteE
Bosporan Kingdom: https://youtu.be/ltikjXUiAC4
Ancient Greek State in Bactria: https://youtu.be/IQATsepKoLE
The Greco-Chinese War Over the Heavenly Horses: https://youtu.be/g6Rphg_lwwM
Ancient Greek Kingdom in India: https://youtu.be/ZxJk4KHZxi8
Ghaznavids: https://youtu.be/yJ91rv0xdWM
Huns: https://youtu.be/bFpQjWtpHcM
White Huns: https://youtu.be/JJWddbCUZLQ
Gokturks: https://youtu.be/BChpoa_IuQs
Yuezhi: https://youtu.be/2KdM6AlyLUY
Seljuks: https://youtu.be/P79ECnISamo
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The video was made by Arb Paninken, while the script was developed by Georgi Kolev. This video was narrated by Officially Devin (https://www.youtube.com/channe....l/UCU0-VII-V376zFxiR & https://www.youtube.com/channe....l/UC79s7EdN9uXX77-Ly
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Correcting a mistake and learning a bit about ion size. Created by Sal Khan.
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Chemistry on Khan Academy: Did you know that everything is made out of chemicals? Chemistry is the study of matter: its composition, properties, and reactivity. This material roughly covers a first-year high school or college course, and a good understanding of algebra is helpful.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
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Scientific evidence suggests that the secret to thriving students and a good education are amazing teachers. To teach with us, gift a video or if you want Sprouts to make videos that teach your student or employees, contact us. Just visit http://patreon.com/sprouts
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4 GREAT TEACHERS
Michael J. Sandel teaching Justice
https://www.youtube.com/watch?v=kBdfcR-8hEY
Robert Sapolsky teaching Introduction to Human Behavioral Biology
https://www.youtube.com/watch?v=NNnIGh9g6fA
Walter Lewin teaching Physics
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Mr. Hester Managing a Classroom
https://www.youtube.com/watch?v=geLvLd3uosk
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Source:
Eric Hanucheck
http://hanushek.stanford.edu
Raj Chetty
Professor of Economics, Stanford University
http://www.rajchetty.com/chett....yfiles/value_added.h http://www.equality-of-opportu....nity.org/assets/docu
Cold Calling
https://www.youtube.com/watch?v=PARfIwF215k&list=PLPkJlPMF7vNsn8UmmQQwIC4sJYhQ2krrT&index=2
Sposato School of Education
http://www.sposatogse.org/
Teachers Effectiveness
http://scholar.harvard.edu/fil....es/fryer/files/dobbi
Time Spend by Principles
https://web.stanford.edu/~sloe....b/papers/Principal%2
What makes Teaching Great
http://www.suttontrust.com/wp-....content/uploads/2014
What Matters in School is Good Teaching
https://www.economist.com/news..../leaders/21700383-wh
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Inside neutron stars we can find the weirdest and most dangerous substance in the universe: Strange matter. What is strange matter, how dangerous is it and what can it tell us about the origin of the universe?
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Help us caption & translate this video!https://www.youtube.com/timedtext_cs_panel?c=UCsXVk37bltHxD1rDPwtNM8Q&tab=2
I asked ChatGPT to create a rectangular triangle in GeoGebra, using only basic drawing tools. It did not find a correct solution.
Previous try using GPT 3.5: https://www.youtube.com/watch?v=DKV_XcZKg0A
Prompt: "Give me the steps in GeoGebra to draw a rectangular triangle. Use only the following tools: point, polygon, intersect, line, segment, circle with center through point, polygon. Make sure each step uses only elements that have been created before. Use wolfram for help."
Model: ChatGPT Jan 12 Version (GPT 4)
GeoGebra version: GeoGebra Classic 5
Music: Compilerbau - Fragments Of Bach I (https://soundcloud.com/compile....rbau/fragments-of-ba
#chatgpt #geogebra #geometry #ai
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/cc-seventh-grade-
The naming of an angle is related to the line segments that create it. We'll also learn about the angle's vertex. Come on. Let's do this.
Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/v/measuring-angles-in-degrees?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry
Missed the previous lesson?
https://www.khanacademy.org/math/geometry/intro_euclid/v/identifying-ray?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry
Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
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Educational video for children to learn how the human ear works. Learn where the three tiny bones are and what is the function of the cochlea. We're also going to give to give you lots of practical ear-care tips! This video belongs to a larger collection of Science videos for children to learn in a fun way. Excellent resource for elementary education.
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For the best selling history themed tabletop games head over to warlord games and check out the Naval warfare in the Black Powder series!
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This type of projectile was particularly effective against the sails, masts, and rigging of a ship, shredding and tearing them apart.
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Achaidh Cheide - Celtic by Kevin MacLeod is licensed under a Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/)
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Kings of the Sea: Charles II, James II & the Royal Navy
By J. D. Davies
Ship Decoration, 1630–1780
By Andy Peters
Pepyss Navy: Ships, Men and Warfare, 1649–89
By J. D. Davies
Artillery Through The Ages: A Short Illustrated History Of Cannon, Emphasizing Types Used In America
by Albert C. Manucy
Determining the projection of a vector on s line
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/expressing-a-projection-on-to-a-line-as-a-matrix-vector-prod?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/unit-vectors?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
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Learn how chatbots work and how to build one for your business in this case study.
AI Casefile Playlist: https://www.youtube.com/watch?v=zKGhV-I250o&list=PL5oju95YSpTV69RmprRJV_YUswBJo2799
AI chatbots aren’t just for tech experts anymore. With the right tools and guidance, anyone can build a chatbot that answers questions, automates tasks, and improves customer experience.
Looking for an easy way to get started with AI education and build your own chatbot—without needing to code? You’re in the right place. In this video, we follow Olivia, a customer service professional, as she explores how AI chatbots can transform everyday work and help her grow her career. Whether you’re working in retail, freelancing, or just curious about automation, this AI education chatbot tutorial is the perfect entry point.
Olivia learns step-by-step how to create a chatbot using IBM Watsonx Assistant—no coding required. This AI education chatbot journey shows you how to go from complete beginner to confident chatbot builder.
If you've ever searched for “how to make money with AI”, “AI tools for work,” or “chatbot training tutorial,” this video is for you. We break it down in clear, simple steps so you can start your own AI education chatbot project today. Stick around to learn how to deploy your bot on websites, mobile apps, and even Facebook Messenger.
Meet Olivia, a 25-year-old working in customer service and bookkeeping at a small flower shop that serves customers both in-store and online. She’s sharp, organized, and well-liked—but like many, she’s hearing the buzz: “AI is coming for your job.”
Instead of panicking, Olivia gets curious.
She starts with the basics: What is a chatbot? A chatbot is a digital assistant that simulates human conversation. It can answer FAQs, provide information, and even help customers choose the perfect bouquet. By automating these repetitive tasks, Olivia realizes she can save time, reduce errors, and focus on meaningful parts of her job.
But Olivia doesn’t stop at basic replies. She discovers action workflows—smart sequences that let her chatbot guide users through tasks like finding store hours or making product suggestions. These workflows are driven by action variables (temporary data used during a task) and session variables (data that persists across conversations). This combo creates more intelligent and user-friendly interactions.
As she dives deeper, Olivia learns about decision-tree bots (structured and predictable) vs. generative AI bots (flexible and conversational). By blending both, she designs a hybrid assistant that feels responsive and personal.
Using IBM Watsonx Assistant, Olivia builds, tests, and deploys her chatbot across web, mobile, and messaging apps. With no need to code, she customizes the design, integrates APIs, and even installs the chatbot on her shop’s WordPress blog. Now, her assistant handles orders, answers questions 24/7, and improves customer satisfaction.
Along the way, Olivia answers key questions many people ask:
How do chatbots actually work?
Do I need to be a developer to use one?
Can chatbots help me at my job or business?
How can I earn or save money with AI?
The answer? Yes. Olivia’s story shows that chatbots aren’t job-stealers—they’re power tools. Whether you work in retail, support, freelancing, or run a side hustle, a well-trained chatbot can save hours, scale your service, and increase earnings.
#NoCodeAI
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#worksmarterwithai
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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/linear-algebra/ve
Parametric Representations of Lines in R2 and R3
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/linear_combinations/v/linear-combinations-and-span?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/vectors/v/intro-unit-vector-notation?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channe....l/UCGYSKl6e3HM0PP7QR
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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/hu....manities/world-histo
Learn about the outbreak of World War I. Created by Sal Khan.
Practice this yourself on Khan Academy right now: https://www.khanacademy.org/humanities/world-history/euro-hist/world-war-i-tutorial/e/world-war-I-causes?utm_source=YT&utm_medium=Desc&utm_campaign=worldhistory
Watch the next lesson: https://www.khanacademy.org/humanities/world-history/euro-hist/american-entry-world-war-i/v/blockades-u-boats-and-sinking-of-the-lusitania?utm_source=YT&utm_medium=Desc&utm_campaign=worldhistory
Missed the previous lesson? https://www.khanacademy.org/humanities/world-history/euro-hist/world-war-i-tutorial/v/assassination-of-franz-ferdinand-by-gavrilo-princip?utm_source=YT&utm_medium=Desc&utm_campaign=worldhistory
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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Learn the letter V with Ollo the Elephant from Khan Academy Kids!
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The attempted unification of church doctrine by Constantine through the Council of Nicaea. Especially resolving the Arian Controversy (based on the views of Arius of Alexandria). The Nicene Creed. Seeds of eventual schism in the church.
Missed the previous lesson? Watch here: https://www.khanacademy.org/hu....manities/world-histo
World History on Khan Academy: From the earliest civilizations to the modern world, geography, religion, trade, and politics have bound peoples and nations together — and torn them apart. Take a journey through time and space and discover the fascinating history behind the complex world we inhabit today.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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Rosdely Ciprian, 16, is an exceptional debater and now a judge of the craft. She’s been perfecting her impressive skills since the sixth grade. Her talent has taken her to Broadway, where she debated on stage in the play, “What the Constitution Means to Me,” now streaming on Amazon Prime Video. With debates at the forefront of the presidential election, Ciprian says “always have your sources” and “always let your opponent talk when it's their turn.” Inside Edition Digital’s Leigh Scheps has more. #InsideEdition
Want to beat blackjack? It all starts with learning how to play. In this video, professional Blackjack players Colin Jones and "Loudon Ofton" break down the objective of blackjack, how to play it, as well as how it is possible to turn the tables on the casino and beat the game.
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00:00 Intro
00:20 Blackjack Rules / How To Play
03:57 Example Rounds of Play
05:49 When to Hit / Stand / Double / Split
09:57 What is Insurance? or Surrendering?
11:59 What Else Do I Need To Know to Win?
Some limit exercises
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Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/limits_topic/old-limits-tutorial/v/limit-examples-part-2?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus
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Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/linear-algebra/ve
Parametric Representations of Lines in R2 and R3
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/linear_combinations/v/linear-combinations-and-span?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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