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

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Practice Your Spanish With Chateo - a Spanish-speaking chatbot! | Get a discount off your first 6 months with code CHATEOBOT | Sign up at: https://www.senorjordan.com/chat
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See explanation on Ojalá here:
https://www.youtube.com/watch?v=dEJdxXMpoTY

Word bank coming soon!

Join my AI Masterclass here: https://academy.dhruvrathee.com/aimasterclass
Learn 25+ AI Tools and upskill yourself.

Is AI the end of human creativity—or just holding up a mirror to it? This eye-opening video dives into AI-generated art, and shocking truths about how much of Indian cinema is "inspired." From Jiddu Krishnamurti and Mark Twain's views on Human Creativity to Bollywood’s copy-paste formula, we question what originality really means. Can true creativity survive in a world where machines learn faster than humans feel?

Link to the mentioned videos:
Internet will NEVER be the Same Again! | Rise of AI Videos | Dhruv Rathee: https://youtu.be/rWpiYvLHmzU?si=BjHqwym4lht-uAQG
---------------------------------------------

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💡In case this video has any factual mistakes, it will be written down on this page: https://dhruvrathee.com/corrections

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Get started with lingoda today and use my code JONESFEB for $25 off: https://try.lingoda.com/LanguagejonesLingoda

Stop using LLMs like a "deranged therapist" and start using them like a linguist. 🧠

We hear about ChatGPT and AI nonstop, but let’s be honest: most people are using them in completely unhinged ways. In this video, I’m putting the big four—ChatGPT, Gemini, Perplexity, and Claude—to the test to see which one actually helps you acquire a language and which one is just a glorified autocomplete.
As a PhD linguist, I’m breaking down the morphosyntax, the feedback loops, and the hallucination rates of these models. Whether you’re a self-study polyglot or just trying to pass your intro classes, here is the objective truth about AI for language learning in 2026.
What We Cover:
• 0:00 Introduction
• 1:05 The unhinged way we use LLMs
• 2:10 I’m launching a course! Sign up for updates at https://www.languagejones.com/accelerator
• 2:50 Lingoda’s winter sale: https://try.lingoda.com/LanguagejonesLingoda
• 4:05 What’s wrong with LLMs
• 5:45 How I evaluated LLMs
• 8:15 Do they get the facts right? Hallucinated verb conjugations
• 12:00 Vocabulary Quality
• 13:00 Transliteration
• 13:53 Volume
• 14:50 Formatting
• 15:25 Images: Bad, worse, and weird
• 17:21 Overall usefulness of content
• 18:10 Grammar explanations
• 19:30 Overall Comparison
• 20:08 My personal winner and runner up

Links & Resources
• My Course: The Linguistics Blueprint: https://www.languagejones.com/blueprint
• The Language Accelerator: https://www.languagejones.com/accelerator

#LanguageLearning #AI #Linguistics #ChatGPT #GeminiAI #Polyglot #LanguageJones #EdTech

"History of Russia in 100 Minutes" is a crash course for beginners. Here you will find the complete history summarized and retold in simple language with accurate dates, the most relevant names and essential concepts. After finishing the course, you will know:

- The basic characteristics of Russian history in different epochs
- The 54 most important rulers and 106 historical persons in Russian history
- 126 key dates and events in Russian history
- The basic terms and concepts of Russian history

The text is accompanied by numerous online resources:
- 20,000 pictures
- 700 videos
- 3,500 songs
- 100 podcast episodes

All that is available via the smarthistories.com website.


http://smarthistories.com/


Narrated by: Sammi Bold
Written by: Tanel Vahisalu
Edited by: Madis Maasing and Kerry Kubilius
Proofread by: Tony Burnett
Graphic Art by: Mehak Zaib Suddle

Video:
“Rise of Catherine the Great” by Paul Czinner, Alexander Korda (1934)

Music:
"Tchaikovsky (Part II)" and "Crocodile Ghena's Song" (1995) by J.M.K.E.
https://www.discogs.com/JMKE-Sputniks...

- - - - - - - - - -

CATHERINE THE GREAT

The reign of Catherine II (Catherine the Great) is known to history as the “Age of Enlightened Absolutism,” in Russia. A whole generation of people grew up enjoying freedom of speech, political stability, and great victories.

BACKGROUND
After the death of Elizabeth, her nephew, Peter III, from Northern Germany ruled disastrously. His wife, Sophie Friederike Auguste, was a pretty German princess who had been invited to Russia while still very young. She converted to Orthodoxy, learned the Russian language, and took the name Catherine. In 1762, she launched a coup against her husband and became the Empress of Russia, known as Catherine the Great.

ENLIGHTENED MONARCH
Catherine continued Peter the Great’s line of modernization, and she strongly supported education and culture. She prepared drafted laws based on the views of the Enlightenment, but the greater part of her ambitious plans, including the abolition of serfdom, led nowhere.

PATRON OF NOBILITY
The great Administration Reform of 1775 increased the administrative power of the nobility. Courts and police institutions were established. The reform significantly increased the effectiveness of local government in Russia.

FOREIGN POLICY
In the beginning, Catherine’s foreign policy was in the hands of Nikita Panin. The commanders Alexander Suvorov, Fyodor Ushakov, and Grigory Potemkin, greatly expanded Russia’s territory in the south and west. In 1784, Crimea was taken from the Ottomans, and the three partitions, formed in 1772, 1793 and 1795, respectively, completely wiped Poland off the map.

PUGACHEV'S REBELLION
Catherine supported the Enlightenment only to a certain extent. She denounced the French Revolution as a brutal act against monarchy.

Although Catherine tried to improve the situation of Russian peasants, these attempts were mostly futile and caused unrest. In 1773, the greatest armed revolt in Russia, constituting 100,000 Cossacks, led by Yemelyan Pugachev, who claimed that he was actually Peter III, was put down ruthlessly. Pugachev was publicly executed.

Division can be done instantly using this amazing math trick!
Moving from left to right trick can be done accurately and faster then a calculator.
In the example provided we will divide 9 into 316249. Amazingly to do this we will not use any division, nor will you have to use your nine times table, instead we will use addition to answer this division question!
This video is part three in a series of three, and leads to how to do long division the fast and easy way!

To donate to the tecmath channel:https://paypal.me/tecmath

To support tecmath on Patreon: https://www.patreon.com/tecmath

To buy tecmath mechandise: https://teespring.com/stores/tecmath-store

🎵 Set sail with us on an exciting voyage through the galaxy of Nursery Rhymes! 🎵

Dive into a vibrant 3D animated video showcasing classics like 'Wheels on the Bus' 🚌, 'Baby Shark' 🦈, 'Old MacDonald Had a Farm' 🐄, and 'Rain Rain Go Away' ☔. Our animated nursery rhymes are sure to entertain, educate, and inspire your little ones.

From peppy toddler tunes 🎶 to soothing bedtime melodies 🌙, our collection ensures learning is a joyful experience. Our channel offers an array of kids' videos that make learning a fun adventure, perfect for anyone who loves a good sing-along.

Join us on this musical odyssey, perfect for all ages. Don't forget to subscribe to Kids TV for more captivating children's music and educational content. Enjoy the learning journey! 😃

#wheelsonthebus, #cocomelon, #babysong, #kidssongs #nurseryrhymes #childrensmusic #educationalvideos #3danimation #kidslearning #singalong #familyfriendly #kidstv #preschoollearning #kidsentertainment #kidsyoutube"

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Does your toddler have a speech delay? Talk to your pediatrician and also call early intervention! The sooner you get help, the better. Definitely try to get speech therapy for your child.

We hope our videos are also helpful for your little one! Ms Rachel's son had a speech delay, and she became very passionate about trying to help toddlers with their language development.

Learn To Talk for Toddlers videos show First Words and functional speech for babies, toddlers, 1 year olds, 2 year olds, 3 year olds and older! We show a mouth close-up, which may be helpful to children with speech delays and apraxia. This video focuses on over 25 first words! Ms Rachel is a master at encouraging speech

In this toddler learning video we show many common first words and functional words that can help toddlers communicate what they need and want.

Words focused on include: Mama, Dada, Hi, Me, More, Go, Help, Eat, Open, I, Want, No, Ya, Mama, Dada, Ball, On, One, Two, Three, Done, Banana, Teddy Bear, Baby, Bubble, Down, Tummy, Peek-A-Boo, Bye.

As well as speech practice sessions, we introduce simple songs that help children with gestures and language. Gestures and imitation are important skills for toddlers! We also demonstrate another important skill for toddlers, pretend and imaginative play. Our videos have also been helpful for children with autism.

If you think your child has a speech delay, definitely talk to your pediatrician. You may qualify for free speech therapy through your state's early intervention program. You can also get evaluated by a speech therapist.

Rachel is not a speech therapist, but on several videos she has worked with speech therapists to share helpful techniques for speech practice.

"Georgie" puppet Copyright 2016 - David Fino & The Brooklyn Puppet Conspiracy. Used with Permission.

On our YouTube page we also have more baby learning videos, toddler learning videos and preschool learning videos. In our educational videos for babies, toddlers and preschoolers, we work on speech and language, milestones, gestures, baby sign language, pretend play, flash cards, social emotional learning, dramatic play, art, music, math, science, circle time, finger plays, singing, dancing, exercises, sensory play and more!

Rachel has worked with children with special needs including autism, down syndrome, speech delays, apraxia, cerebral palsy and global developmental delays. She believes all children are smart, important, gifted, valuable and our teachers.

We put your baby first and not entertainment value. That is why there is no loud music during the presentation of words.

#learntotalk #learntotalkfortoddlers #firstwords #apraxia #speechdelay #firstwordsforbabies #firstwordsfortoddlers #educationalvideos #flashcards #babies #toddlers #1yearold #2yearold #3yearold #milestones #babiesfirstwords

Rachel has taught preschool music to young kids, toddlers, and babies and has a master's in music education from NYU. She has also been a toddler teacher and has a sweet 2-year-old boy who inspired her online baby music classes and learning videos!

♥︎ Subscribe to support our YouTube channel https://bit.ly/2YldegF
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Our video are great for your 1 year old, 2 year old, 3 year old, 4 year old and 5 year old! Even parents enjoy the educational videos we create. Our videos are wonderful for preschoolers, kindergarteners and even elementary students. Our videos are in English and we purposefully speak slowly and clearly for optimal learning. We hope you enjoy our English learning videos for toddlers.

What will the future of education look like in a world increasingly shaped by AI?

Join Steve Levitt, Freakonomics co-author and founder of The Levitt Lab, a high school reimagining education, and Ben Gomes, Chief Technologist, Learning at Google in a conversation about the potential of AI in education. #AI #Education #Learning

Watch more: https://www.youtube.com/playli....st?list=PL590L5WQmH8

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In which John Green teaches you about the Cold War, which was occasionally hot, but on average, it was just cool. In the sense of its temperature. It was by no means cool, man. After World War II, there were basically two big geopolitical powers left to divide up the world. And divide they did. The United States and the Soviet Union divvied up Europe in the aftermath of the war and then proceeded to spend the next 45 years fighting over the rest of the world. It was a great ideological struggle, with the US on the side of capitalism and profit, and the USSR pushing Communism, so-called. While both sides presented themselves as the good guy in this situation, the COLD reality is that there are no good guys. Both parties to the Cold War engaged in forcible regime changes, built up vast nuclear arsenals, and basically got up to dirty tricks. If you had to pick a bad guy though, we would point out that the USSR had no intention of bringing Laika the Cosmonaut Dog home alive. That poor dog never had a shot.

Thanks to Raoul Meyer for the YUGOGAL photo.

Chapters:
Introduction: The Cold War 00:00
The conflict between the USA and USSR 0:51
Soviet Sphere of Influence post-WWII 2:00
An Open Letter to Joseph Stalin 3:00
The Marshall Plan, the Berlin Wall, and NATO 4:04
The Nuclear Arms Race 5:16
The Hot Parts of the Cold War 6:00
The Lukewarm Parts of the Cold War 7:10
First-World, Second-World, and Third-World Divisions 7:46
The Failures of Soviet Socialism 9:06
The End of the Cold War 9:27
Credits 11:44

Want to learn more about the Cold War? Check out these other Crash Course videos:
The Cold War: Crash Course US History #37 https://www.youtube.com/watch?v=9C72ISMF_D0
The Cold War in Asia: Crash Course US History #38 https://www.youtube.com/watch?v=Y2IcmLkuhG0
George HW Bush and the End of the Cold War: Crash Course US History #44
https://www.youtube.com/watch?v=L-K19rVDxoM
The Cold War and Consumerism: Crash Course Computer Science #24
https://www.youtube.com/watch?v=m8i38Yq1wX4
Post-War Rebuilding and the Cold War: Crash Course European History #41
https://www.youtube.com/watch?v=-rkIqtV07HE

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Visit https://www.woloafric.com/courses for more lessons.
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Wolo, Smart Way to Learn.

We promise to deliver world-class tuition for Senior High School Students and Skills training for corporate individuals.

Wolo, Smart way to learn!

You can now share Google Gemini Gems 🎉
That means reusable AI prompts for lesson planning, feedback, differentiation, and student support—shared across teams and classrooms.
Build once. Share widely. Scale impact.

Have fun singing the Finger Family song (a.k.a. Daddy Finger Song) with your kids! 🖐️ Join Lucas 🦁, Ruby 🐰 and their friends as you sing nursery rhymes everyone will love, including the five finger family song! 🥰 It's easy to learn, and tons of fun to sing, especially for preschoolers, toddlers, and babies! ✨

If you've never heard the Finger Family song, you can learn the lyrics in just a few seconds! 📌 It starts by showing children the "daddy finger" (thumb), then goes through the whole family, teaching kids about daddies, mommies, babies, and siblings, all with an adorable finger dance your kids will love to mimic. ✔️ Not only will it help children learn about families, but it's a great way to get them moving and build hand-eye coordination! 😃

⦿ Sing along with your children, lyrics provided below:

Daddy finger, daddy finger, where are you?
Here I am, here I am,
How do you do?

Mummy finger, mummy finger, where are you?
Here I am, here I am,
How do you do?

Brother finger, brother finger, where are you?
Here I am, here I am,
How do you do?

Sister finger, sister finger, where are you?
Here I am, here I am,
How do you do?

Baby finger, baby finger, where are you?
Here I am, here I am,
How do you do?

👉 Like these sing-along songs and nursery rhymes? 🎯 SUBSCRIBE to our channel for more ultra HD 4K nursery rhymes and kids songs! 👍 Be sure to LIKE and SHARE so more families can discover free sing-along kids songs by RV Kids! 🔥

🔗 Checkout our website for educational kids apps, coloring pages & more - www.rvappstudios.com

Copyright © RV AppStudios

#FingerFamily #BabySongs #NurseryRhymes

This tutorial explains how we can use the addition property of zero and the additive inverse property, to take an expression and write it in a different form.

Join this channel to get access to perks:
https://www.youtube.com/channe....l/UCn2SbZWi4yTkmPUj5

:)

The Land Back movement is exactly what it sounds like: Native Americans want their land … back. But it’s also a whole lot more than that. In this episode of Crash Course Native American History, we explore what the Land Back movement does, how it works, and what it means for our shared future on this planet.

Introduction: 1492 Land Back Lane 00:00
Land Back & Land Acknowledgements 0:40
Settler Rent 2:00
The Jemez Pueblo Tribe 3:17
Environmental Impact 4:14
Haudenosaunee Activism 7:04
Review & Credits 9:26

Sources:
https://docs.google.com/docume....nt/d/1g1BpQk_2qXtFeQ

Want to know more about how this series was made? Learn more here: https://docs.google.com/docume....nt/d/17yp3u28s40Tdjy
***
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Thanks to the following patrons for their generous monthly contributions that help keep Crash Course free for everyone forever:
oranjeez, Jason Terpstra, Chelsea S, Alan Bridgeman, Roger Harms, DexcilaDou, Krystle Young, Allison Wood, Stephen Akuffo, Katrix , Gina Mancuso, Shruti S, Martin G. Diller, Matthew Fredericksen, Brandon Thomas, Breanna Bosso, Ken Davidian, UwU, Jennifer Wiggins-Lyndall, Samantha, David Fanska, Kristina D Knight, Andrew Woods, Elizabeth LaBelle, SpaceRangerWes, Matt Curls, Quinn Harden, EllenBryn, Johnathan Williams, Leah H., Laurel Stevens, Steve Segreto, Michael Maher, Liz Wdow, Toni Miles, Perry Joyce, Evan Nelson, Katie Hoban, Mitch Gresko, Kevin Knupp, Kyle & Katherine Callahan, Tanner Hedrick, Emily Beazley, Jack Hart, Rie Ohta, Dalton Williams, Scott Harrison, Barbara Pettersen, AThirstyPhilosopher ., Thomas Sully, Bernardo Garza, Jason Rostoker, Rizwan Kassim, Indija-ka Siriwardena, Emily T, Ian Dundore, Joseph Ruf, Alex Hackman, Thomas, Constance Urist, team dorsey, Stephen McCandless, Triad Terrace, Erminio Di Lodovico, Evol Hong, Luke Sluder, Eric Koslow, Katie Dean, Tandy Ratliff, Jennifer Killen, Jason Buster, Trevin Beattie, Wai Jack Sin, Caleb Weeks, Nathan Taylor, Siobhán, Les Aker, Barrett Nuzum, John Lee, Ken Penttinen, Sarah & Nathan Catchings, Pietro Gagliardi, ClareG, Duncan W Moore IV
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Watch more: https://youtu.be/YMbhCGgCzVI

Is education preparing students for a world dominated by AI? This documentary investigates the growing gap between what schools teach and what the future job market demands. We delve into the critical skills needed to succeed in an AI-driven world and ask if current educational systems can adapt quickly enough.

We explore:

The essential skills for the AI age: computational literacy, critical thinking, innovation, and social intelligence.
The slow pace of educational reform and the challenges of integrating new technologies.
The digital divide and unequal access to learning resources.
The potential of AI to personalize learning and create more engaging educational experiences.
The importance of entrepreneurship and lifelong learning in a rapidly changing world.
Don't miss this crucial discussion about the future of learning! #Education #AI #FutureOfWork #SkillsGap #EdTech #AIEducation #DigitalEducation #LearningTechnology #EducationReform #InnovationInEducation #AIinEducation

WITH:
Gunay Kazimzade, Cedric Sauviat, Fabian Westerheide, Annika Nadja Smit, Thiébaut Weber, Daniel Göhring, Florian Buttollo, Aljoscha Burchardt, Matthias Wählisch, Martin Schlüßer, Asheesh Advani, Saadia Zahidi, Mariéme Jamme, Raul Rojas, Holger Behnsen, Hadi Partovi, Michael Feindt and Yuval Noah Harari and Zach Klein.

SPECIAL THANKS TO:
@wef @slush @Emarsys @weizenbauminstitut @etucces @dfkivideo @FreieUniversitaetBerlin @EU_EDPS​

Pre-order our book YOU ARE AN ARTIST (which includes new assignments!) here: http://bit.ly/2kplj2h

In which we visit artist Kate Gilmore in her Brooklyn studio and receive the assignment to Walk on It.

INSTRUCTIONS - Walk On It

1. Find a big piece of wood or board

2. Paint it heavy with a color that you love

3. Put on a fabulous pair of shoes and walk on it. When it looks cool, you're done.

4. Upload it using #theartassignment

5. Fame and glory (your work might be in a future episode)

Learn more about Kate Gilmore: www.kategilmore.com
Watch an excellent video by MOCA Cleveland: http://vimeo.com/66081903
And here's one of me talking to Kate back in 2010 when she was commissioned to create a work for the Indianapolis Museum of Art: http://youtu.be/C3PjWmUJZsM

Also mentioned:
Jackson Pollock: http://youtu.be/6cgBvpjwOGo
Lynda Benglis: http://whitney.org/WatchAndLis....ten/Artists?play_id=
Bruce Nauman: http://www.pbs.org/art21/artists/bruce-nauman
Process Art: http://www.artspace.com/magazi....ne/art_101/process_a

Another YouTube #shorts from Dr. Joe! Subscribe for more fun science stories.

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Discover hundreds of never-before-seen resources! Create your free account at https://my.happylearning.tv/ and start learning in the most entertaining way.

What are you waiting for? We all know how to read and write but... Did you know how it all started?
?? What was the first ever paper called?
?? Where did our ancestors write if they didn't have paper?
?? What does your favorite pen or pencil look like?

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Recommended video: Prehistory
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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!

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