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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
Introduction to the cross product
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/dot_cross_products/v/proof-relationship-between-cross-product-and-sin-of-angle?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/dot_cross_products/v/defining-a-plane-in-r3-with-a-point-and-normal-vector?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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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/ap-calculus-bc/bc
The ratio test is a most useful test for series convergence. It caries over intuition from geometric series to more general series. Learn more about it here.
AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test
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.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy's AP Calculus BC channel: https://www.youtube.com/channe....l/UC5A2DBjjUVNz8axD-
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The word "are" is spelled a-r-e. The word "are" is a form of the word "be," which can describe the quality of a person, place, or thing. These apples are tasty!
Learn the sight word "are" with the Khan Academy Kids characters. The fun example, easy-to-remember definition, and cute illustrations will help kids remember the word any time they come across it.
Visit us at http://www.khankids.org to learn more about Khan Academy Kids, a free educational app for preschool through 2nd grade.
Available on Google Play, Apple, and Amazon app stores:
➡️ http://khan.co/KhanKids-YT-Google
➡️ http://khan.co/KhanKids-YT-Apple
➡️ http://khan.co/KhanKids-YT-Amazon
You can also access other sight words videos on our Sight Words playlist here: http://khan.co/KhanKids-SightWords.
Subscribe to our channel for more videos like this.
Learn more counting, addition, and subtraction lessons in the FREE Khan Academy Kids app! https://go.learn.khanacademy.o....rg/khanacademy/YouTu
Peck learns subtraction by counting backward with strawberries. Way to count on, Peck!
Visit us at http://www.khankids.org to learn more about Khan Academy Kids, a free educational app for preschool through 2nd grade available on Apple, Google Play, and Amazon app stores.
You can also access other videos on our Addition and Subtraction playlist here: http://khan.co/KhanKids-AdditionSubtraction
Subscribe to our channel for more videos like this.
Questions? Reach our team at khankids@khanacademy.org.
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Created by Daniel Turner (B.A. (Hons) in History, University College London)
Though we often think of the Vikings of Scandinavia as being barbarians, when it came to warfare they were quite advanced warriors, as well as being highly practical. So they tended to favour weapons that served a purpose in everyday life, as well as on the battlefield.
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Credit:
Created by Daniel Turner (B.A. (Hons) in History, University College London)
Script: Conan White
Narrator:
Bryan 'Lazlo' Beauregard
Music Credit
Crusade - Video Classica by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/by/4.0/
Source: http://incompetech.com/music/r....oyalty-free/index.ht
Artist: http://incompetech.com/
Sources:
Weapons of the Viking Warrior
By Gareth Williams
The Viking Age: The Early History, Manners, and Customs of the ..., Volume 2
By Paul Belloni Du Chaillu
Ancient Weapons in Britain
By Logan Thompson
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Truth is often stranger than fiction, and sometimes a real life tale is so outlandish, that people are often left to wonder “why hasn’t this been made into a movie.” This is one of those stories.
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Credit:
Show Created by Daniel Turner (B.A. (Hons) in History, University College London)
Script: Robert de Graff
Narrator: Jared Sager
Where did Vladimir Putin come from? What was Putin’s education? Who pushed Putin to pursue a meteoric rise to Prime Minister and President of the largest country in the word? Watch Putin’s history unfold from his modest origins to the dominant figure he is today.
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Credit:
Created by Daniel Turner (B.A. (Hons) in History, University College London)
Narrator:
Bryan 'Lazlo' Beauregard
Sources:
· Sebestyen, Victor (2018), Lenin the Dictator
· Truscott, Peter (2005). Putin's Progress: A Biography of Russia's Enigmatic President, Vladimir Putin
· Lynch, Allen. Vladimir Putin and Russian Statecraft
· Vladimir Putin; Nataliya Gevorkyan; Natalya Timakova; Andrei Kolesnikov (2000). First Person: An Astonishingly Frank Self-Portrait by Russia's President Vladimir Putin
· Rosefielde, Steven; Hedlund, Stefan (2009). Russia Since 1980
· Dawisha, Karen (2015). Putin's Kleptocracy: Who Owns Russia?
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Credit:
Created by Daniel Turner (B.A. (Hons) in History, University College London)
Script: Dejan Milivojevic
Narrator:
Chris Kane
https://vocalforge.com/
Sources:
Cole, Roger, and Richard Belfield. SAS Operation Storm. Hodder & Stoughton, 2011.
White, Rowland. Storm Front. Corgi, 2012.
“Battle of Mirbat: The near Alamo of the Special Air Service.” SOFREP, 5 Mar. 2020, sofrep.com/news/special-air-services-secret-war-oman-part-5/
Malcher, Author Alan. “The Battle of Mirbat, Oman, 19 July 1972: 22nd Special Air Service Regiment.” Alan Malcher, 15 Dec. 2021,
Thanks to World of Tanks for sponsoring this video! Click here to claim your free premium World of Tanks starter Pack: https://tanks.ly/3mIQgyd
One of the most iconic visual elements of the Second World War are German panzers blitzing their way across enemy territory, leaving a trail of death and destruction in their wake.
During the First World War, German tanks had a less than auspicious start. Their first attempt at a tank design was the A7V, a clunky metal box on tracks, a far cry from the formidable vehicles of a quarter century later.
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Credit:
Show Created by Daniel Turner (B.A. (Hons) in History, University College London)
Script: Robert de Graaf
Narrator:
Chris Kane
https://vocalforge.com/
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Land reform, where estates had been taken from rich landowners and redistributed to the peasants had taken place shortly after the communists had come to power.
Collectivisation, where peasants lost their own pieces of land and instead worked for wages on land owned by the state had also begun to take place.
Mao believed this was not enough to expand both agricultural and industrial production and instead introduced the second five-year plan in 1958.
This would become known as the ‘Great Leap Forward’.
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Credit:
Created by Daniel Turner
Narrator:
Chris Kane
https://vocalforge.com/
Music Credit:
Decline by Kevin MacLeod is licensed under a Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/)
Source: http://incompetech.com/music/r....oyalty-free/index.ht
Artist: http://incompetech.com/
Sources:
Tombstone. The Untold story of Mao’s Great Famine.
By Yang Jisheng.
Red Inc.: Dictatorship and the Development of Capitalism in China, 1949-2009
By Robert K. Schaeffer
Socialism in China (1919-1965)
By Yu Youjun
Mao's Great Famine: The History of China's Most Devastating Catastrophe, 1958-62
By Frank Dikötter
The Great Famine in China, 1958-1962: A Documentary History
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Thanks to the technological advances of the modern age, in 2023 life is pretty safe. In the past however, many of the things we take for granted now were likely a death sentence for our ancestors.
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Credit:
Show Created by Daniel Turner (B.A. (Hons) in History, University College London)
Script: Jake Leigh-Howarth
Narrator:
Chris Kane
https://vocalforge.com/
Backe, Caleb. "Deadly Beauty Practices In History." 6 March, 2022. Maple Holistics.
BAUS. "Virtual Museum Time Corridor 17th Century". Accessed 27 February, 2023.
CDC. "Syphilis: The Facts." Accessed 27 February, 2023.
CTPA. "Cosmetic Safety." Accessed 27 February, 2023.
De Abreu, Kristine. "Apocalypse Then: The Volcanic Winter of 536AD." July 18, 2022. ExplorersWeb.
Degroot, Dagomar. "Small climate changes can have devastating local consequences – it happened in the Little Ice Age." July 27, 2021. The Conversation.
Eschner, Kat. "Fearing a Smallpox Epidemic, Civil War Troops Tried to Self-Vaccinate." May 1, 2017. Smithsonian.
Finance. "Scotland to Panama Flight Duration." Accessed 27 February, 2023.
Greschko, Michael. "Colossal volcano behind 'mystery' global cooling finally found." August 23, 2019. NationalGeographic.
Grist, Kerry. "Dangerous Beauty: Hazardous Chemicals and Poisons in Historic Cosmetics." 29 July 2022. ScienceMuseumGroup.
Johnson, Ben. "The Darien Scheme." Accessed 27 February, 2023.
Kelly, DB. "The Deadly Great Frost of 1709 Is Still a Mystery." Last modified 13 January, 2022. Grunge.
Lanchester, John. "How the Little Ice Age Changed History." March 25, 2019. The New Yorker.
Laumonier, Lucie. "A Medieval Peasants’ Winter." rused 27 February, 2023.
Maley, Sonny. "The Darien Scheme." May 2005. GLA.
Maloney, T.R., Dilkes-Hall, I.E., Vlok, M. et al. "Surgical amputation of a limb 31,000 years ago in Borneo." Nature 609 (September 2022): 547–551.
Oosthoek, K. Jan. "Little Ice Age." June 5, 2015. EH Resources.
Pattenden, Miles. "Volcanoes, plague, famine and endless winter: Welcome to 536, what historians and scientists believe was the ‘worst year to be alive'." February 1, 2022. The Conversation.
Seladi-Schulman, Jill. "What Is the Periosteum?" Last modified September 26, 2018. Healthline.
Shuster, Sam. "Painless amputation: history of a discovery
that wasn’t made." BMJ (19-26 December 2009).
Smith College. "The Effects of the Little Ice Age (c. 1300-1850)." Accessed 27 February, 2023.
Wischhover, Cheryl. "The Most Dangerous Beauty Through the Ages." December 17, 2013. TheCut.
Zapata, Mariana. "How Civil War Soldiers Gave Themselves Syphilis While Trying to Avoid Smallpox." November 30, 2016. Atlas Obscura.
A rise of protests by students and workers waving Hungarian flags with the communist emblem in the centre cut out arose in Budapest, erupting into active fighting in October 1956.
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Credit:
Narrator:
Chris Kane
http://ckvox.com/
Animation:
Daniel Turner
Artwork:
Daniel turner
Logo of the Warsaw Treaty Organization of Friendship, Cooperation, and Mutual Assistance
CC BY-SA 3.0
Fenn-O-maniC - Own work
https://creativecommons.org/licenses/by-sa/3.0/
Music Credit
The Descent Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0 License
http://creativecommons.org/licenses/by/3.0/
#shorts
This statistics video tutorial explains how to make a histogram using a frequency distribution table.
Introduction to Statistics: https://www.youtube.com/watch?v=XZo4xyJXCak
Arithmetic, Geometric, & Harmonic Mean:
https://www.youtube.com/watch?v=6G6i8vSa8Zs
Simple Frequency Tables:
https://www.youtube.com/watch?v=lyRbCwDDnJo
Relative Frequency Distribution Table:
https://www.youtube.com/watch?v=gq3FPpm2yvA
Cumulative Relative Frequency Table:
https://www.youtube.com/watch?v=6hJGa4Zp62M
_________________________________
Dot Plots and Frequency Tables:
https://www.youtube.com/watch?v=Iu17mY1VfZU
Stem and Leaf Plots:
https://www.youtube.com/watch?v=MUCvUgGfzdo
Side By Side Stem and Leaf Plots:
https://www.youtube.com/watch?v=wkAjnGmRPVo
Histograms:
https://www.youtube.com/watch?v=AndS0RLdxtk
How To Make a Frequency Polygon:
https://www.youtube.com/watch?v=y7Wb9AjbRjo
__________________________________
Quartiles, Deciles, & Percentiles:
https://www.youtube.com/watch?v=40o82o3uNfk
Interquartile Range & Outliers:
https://www.youtube.com/watch?v=STSP8gTSdT8
Skewness & Symmetric Distribution:
https://www.youtube.com/watch?v=U0NZu6f5TMI
Sample Mean and Population Mean:
https://www.youtube.com/watch?v=cmtBUWCC-6A
Mean, Median, & Mode - Grouped Data:
https://www.youtube.com/watch?v=zjHfAhcU6kE
____________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/
This math video tutorial provides a basic introduction into ratio and proportion word problems. Here is a list of examples and practice problems:
Percentage Word Problems: https://www.youtube.com/watch?v=kjpwBu6DmkM
Unit Rates, Ratios, & Proportions:
https://www.youtube.com/watch?v=s0RBRkehzwo
Ratios and Proportions - Word Problems:
https://www.youtube.com/watch?v=JOZSFwuyqok
Ratios and Proportions - SAT Math:
https://www.youtube.com/watch?v=Y4fgwWEGQlg
Ratios and Proportions - Mean & Geometry:
https://www.youtube.com/watch?v=tFCrFa0mDi4
__________________________________
Acid Mixture Word Problems:
https://www.youtube.com/watch?v=e2FAAMlAJ3c
Translating Words to Algebraic Expressions:
https://www.youtube.com/watch?v=QEnFIgN8UBw
Words to Equations - More Problems:
https://www.youtube.com/watch?v=VjPX-XlN7Ok
Consecutive Integers Word Problems:
https://www.youtube.com/watch?v=hPnoxAf60c0
Age Word Problems - Past, Present, Future:
https://www.youtube.com/watch?v=7x7Hl9ztYbk
__________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/
This calculus video provides a basic introduction into the derivatives of inverse trigonometric functions. It explains how to find the derivative of arcsin, arccos, arctan, and arcsec using simple formulas.
Derivatives - Fast Review: https://www.youtube.com/watch?v=5yfh5cf4-0w&t=1s
Derivatives - The Product Rule - f*g:
https://www.youtube.com/watch?v=17X5g9QArTc
Derivatives - The Quotient Rule:
https://www.youtube.com/watch?v=8jVDEcQ0wXk
Derivatives - The Chain Rule:
https://www.youtube.com/watch?v=HaHsqDjWMLU
Derivatives - Composite Functions:
https://www.youtube.com/watch?v=vNXjMTv4vHs
__________________________________
Implicit Differentiation:
https://www.youtube.com/watch?v=xbviQHhU1rA
Derivatives of Inverse Trig Functions:
https://www.youtube.com/watch?v=KbYW9FDm-Zk
Derivatives of Exponential Functions:
https://www.youtube.com/watch?v=yg_497u6JnA
Derivatives of Logarithmic Functions:
https://www.youtube.com/watch?v=Dp9sgIvaKPk
Logarithmic Differentiation:
https://www.youtube.com/watch?v=9z1Dz60mWcQ
___________________________________
Derivatives - Using Logarithms:
https://www.youtube.com/watch?v=VnB59SrT0PY
Derivatives of Inverse Functions:
https://www.youtube.com/watch?v=Hw6ltuCEtuU
Derivatives - Differentiation Rules:
https://www.youtube.com/watch?v=IvLpN1G1Ncg
Derivatives - Function Notations:
https://www.youtube.com/watch?v=7BK_mmYckmI
Derivatives - The Reciprocal Rule:
https://www.youtube.com/watch?v=dsqD5zg9hLY
_________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathSc....ienceTutor/collectio
This calculus video tutorial provides a basic introduction into the quotient rule for derivatives. It explains how to find the derivatives of fractions and rational functions.
Derivatives - Fast Review: https://www.youtube.com/watch?v=5yfh5cf4-0w&t=1s
Equation of the Tangent Line:
https://www.youtube.com/watch?v=5NyeGzbBJQM
Simplifying Derivatives:
https://www.youtube.com/watch?v=3lUOtjkqfQo
Derivatives - The Product Rule - f*g:
https://www.youtube.com/watch?v=17X5g9QArTc
Derivatives - Triple Product Rule - f*g*h:
https://www.youtube.com/watch?v=cUXW9cj_CpE
Derivatives - Quadruple Product Rule - f*g*h*k:
https://www.youtube.com/watch?v=U8u0VGvFgV0
___________________________________
Derivatives - The Quotient Rule:
https://www.youtube.com/watch?v=8jVDEcQ0wXk
Derivatives - The Chain Rule:
https://www.youtube.com/watch?v=HaHsqDjWMLU
Chain Rule With Trig Functions:
https://www.youtube.com/watch?v=ZyWHTWJ2XpM
Chain Rule - Harder Examples:
https://www.youtube.com/watch?v=_1LTThkXvSw
Chain Rule - Triple SQRT(x):
https://www.youtube.com/watch?v=BTuGkPj7ymE
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Derivatives - Composite Functions:
https://www.youtube.com/watch?v=vNXjMTv4vHs
Implicit Differentiation:
https://www.youtube.com/watch?v=xbviQHhU1rA
Derivatives - Inverse Trig Functions:
https://www.youtube.com/watch?v=KbYW9FDm-Zk
Derivatives - Exponential Functions:
https://www.youtube.com/watch?v=yg_497u6JnA
Derivatives - Logarithmic Functions:
https://www.youtube.com/watch?v=Dp9sgIvaKPk
___________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathSc....ienceTutor/collectio
This stoichiometry video tutorial explains how to perform mole to mole conversions from a balanced chemical equation. It contains plenty of examples of mole ratio practice problems. It discusses how to calculate the number of moles reactant that are required to react with the limiting reagent and how many moles of product are expected to be produced using the molar ratio method. This chemistry video also contains examples of balancing chemical equations which are needed before solving any mole to mole stoichiometry problems.
Introduction to Moles:
https://www.youtube.com/watch?v=EowJsC7phzw
How To Calculate The Molar Mass:
https://www.youtube.com/watch?v=c_zHROisdP4
How To Convert Grams to Moles:
https://www.youtube.com/watch?v=irYPta9G_sw
How To Convert Moles to Grams:
https://www.youtube.com/watch?v=Bj3fr5pEn7U
Moles to Atoms Conversion:
https://www.youtube.com/watch?v=mpHQZ1PrkUI
Grams to Molecules Conversion:
https://www.youtube.com/watch?v=Ch16s4kYH1Q
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Grams to Atoms:
https://www.youtube.com/watch?v=RFCtPjZ4Vzk
Moles, Atoms, & Grams Conversions:
https://www.youtube.com/watch?v=i1EPgeu_fJ8
How To Balance Chemical Equations:
https://www.youtube.com/watch?v=iUARzSxcKzk
Stoichiometry - Basic Introduction:
https://www.youtube.com/watch?v=7Cfq0ilw7ps
Avogadro's Number:
https://www.youtube.com/watch?v=74-X94OP2XI
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Limiting Reactant Problems:
https://www.youtube.com/watch?v=IWtkhAv4RTo
Excess Reactant Problems:
https://www.youtube.com/watch?v=-7UloVZFG00
Theoretical & Percent Yield:
https://www.youtube.com/watch?v=hhEfqa_x7RQ
Percent Yield - More Examples:
https://www.youtube.com/watch?v=w1njGAkc8og
Percent Error:
https://www.youtube.com/watch?v=JbEo46uV6d4
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Percent Composition By Mass:
https://www.youtube.com/watch?v=bGmbyztdCHE
Empirical Formula Problems:
https://www.youtube.com/watch?v=JeSSucG-CVw
Empirical Formula - Hydrated Compounds:
https://www.youtube.com/watch?v=gl_QAO5y9Ig
Combustion Analysis:
https://www.youtube.com/watch?v=uvR7zNJ1KoI
Stoichiometry Practice Test:
https://www.youtube.com/watch?v=mP2Yg8alyR0
_______________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathSc....ienceTutor/collectio