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Adding vectors algebraically & graphically
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To add the vectors (x₁,y₁) and (x₂,y₂), we add the corresponding components from each vector: (x₁+x₂,y₁+y₂). Here's a concrete example: the sum of (2,4) and (1,5) is (2+1,4+5), which is (3,9). There's also a nice graphical way to add vectors, and the two ways will always result in the same vector.​​

Subject:
Algebra
Material Type:
Lesson
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
07/07/2021
Ai Weiwei's "Remembering" and the Politics of Dissent
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All art is political in the sense that all art takes place in the public arena and engages with an already existing ideology. Chinese artist, Ai Weiwei, offers an important contemporary example. The news that Chinese artist Ai Weiwei has been detained by authorities has prompted significant concern. Ai Weiwei has ben arrested by the Chinese authorities.

Subject:
Arts and Humanities
Material Type:
Diagram/Illustration
Lecture
Provider:
Khan Academy
Provider Set:
Smarthistory
Author:
Beth Harris
Steven Zucker
Date Added:
07/07/2021
Albrecht Dürer, Self-Portrait (1500)
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CC BY-NC-SA
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In this art history video discussion Beth Harris and Steven Zucker look at Albrecht Durer's "Self-Portrait, 1500." (Alte Pinakothek, Munich).

Subject:
Arts and Humanities
Art History
Visual Arts
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Smarthistory
Author:
Beth Harris Ph.D.
Steven Zucker Ph.D.
Date Added:
07/07/2021
Alexander Mosaic
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This art history video examines the "Alexander Mosaic" c. 100 B.C.E., tessera mosaic from the House of the Faun, Pompeii. This Roman floor mosaic may be based on a lost Hellenistic painting by Philoxenos of Eretria, The Battle of Issus, c. 315 B.C.E.). Museo Archeologico Nazionale, Naples.

Subject:
Arts and Humanities
Art History
Visual Arts
Material Type:
Diagram/Illustration
Lecture
Provider:
Khan Academy
Provider Set:
Smarthistory
Author:
Beth Harris
Steven Zucker
Date Added:
07/07/2021
Algebra: Arithmetic with Polynomials and Rational Expressions
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CC BY-NC-SA
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This site teaches Arithmetic with Polynomials and Rational Expressions to High Schoolers through a series of 4333 questions and interactive activities aligned to 26 Common Core mathematics skills.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Interactive
Provider:
Khan Academy
Provider Set:
Khan Academy
Date Added:
07/07/2021
Algebra: Reasoning with Equations and Inequalities
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CC BY-NC-SA
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This site teaches Reasoning with Equations and Inequalities to High Schoolers through a series of 5909 questions and interactive activities aligned to 36 Common Core mathematics skills.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Interactive
Provider:
Khan Academy
Provider Set:
Khan Academy
Date Added:
07/07/2021
Algebra: Seeing Structure in Expressions
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CC BY-NC-SA
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This site teaches Structure in Algebraic Expressions to High Schoolers through a series of 3482 questions and interactive activities aligned to 26 Common Core mathematics skills.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Interactive
Provider:
Khan Academy
Provider Set:
Khan Academy
Date Added:
07/07/2021
Allston's Elijah in the Desert
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CC BY-NC-SA
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This art history video discussion examines Washington Allston's "Elijah in the Desert", 1818, oil on canvas, 125.09 x 184.78 cm / 49 1/4 x 72 3/4 inches (Museum of Fine Arts, Boston).

Subject:
Arts and Humanities
Art History
U.S. History
Material Type:
Diagram/Illustration
Lecture
Provider:
Khan Academy
Provider Set:
Smarthistory
Author:
Beth Harris
Steven Zucker
Date Added:
07/07/2021
Alma-Tadema's Listening to Homer
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CC BY-NC-SA
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This art history video discussion examines Sir Lawrence Alma-Tadema's "A Reading from Homer", 1885, oil on canvas, (Philadelphia Museum of Art).

Subject:
Arts and Humanities
Art History
Material Type:
Diagram/Illustration
Lecture
Provider:
Khan Academy
Provider Set:
Smarthistory
Author:
Beth Harris
Steven Zucker
Date Added:
07/07/2021
Altdorfer's The Battle of Issus
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CC BY-NC-SA
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In this art history video discussion Beth Harris and Steven Zucker examine Albrecht Altdorfer's "The Battle of Issus," 1529, oil on panel. Alte Pinokothek, Munich.

Subject:
Arts and Humanities
Art History
Visual Arts
Material Type:
Diagram/Illustration
Lecture
Provider:
Khan Academy
Provider Set:
Smarthistory
Author:
Beth Harris and Steven Zucker
Date Added:
07/07/2021
Ambrogio Lorenzetti's Palazzo Pubblico Frescos: Allegory and Effect of Good and Bad Government
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In this art history video discussion Dr. Beth Harris and Dr. Steven Zucker consider Ambrogio Lorenzetti's series of frescos "Allegory of Good Government", "Effects of Good Government in the City and the Country", and "Allegory and Effects of Bad Government in the City and the Country" Siena c. 1337-40. Sala della Pace (Hall of Peace) also known as the Sala dei Nove (the Hall of the Nine), Palazzo Pubblico, Siena.

Subject:
Arts and Humanities
Art History
Visual Arts
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Smarthistory
Author:
Beth Harris and Steven Zucker
Date Added:
07/07/2021
Andrea Mantegna, Camera Degli Sposi
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This art history video discussion examines Andrea Mantegna's "Camera degli Sposi" (Frescos in the ducal palace, Mantua), 1465-74.

Subject:
Arts and Humanities
Art History
Material Type:
Diagram/Illustration
Lecture
Provider:
Khan Academy
Provider Set:
Smarthistory
Author:
Beth Harris
David Drogin
Date Added:
07/07/2021
Andrea Pisano's Reliefs on the Campanile in Florence
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This art history video discussion examines Andrea Pisano, Reliefs for the Campanile in Florence, c. 1336.

Subject:
Arts and Humanities
Art History
Material Type:
Diagram/Illustration
Lecture
Provider:
Khan Academy
Provider Set:
Smarthistory
Author:
Beth Harris
David Drogin
Date Added:
07/07/2021
Antoine or Louis Le Nain, Peasant Family in an Interior
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This art history video discussion examines Antoine or Louis Le Nain's "Peasant Family in an Interior", 2nd quarter of the 17th century, oil on canvas (Musee du Louvre, Paris).

Subject:
Arts and Humanities
Art History
Material Type:
Diagram/Illustration
Lecture
Provider:
Khan Academy
Provider Set:
Smarthistory
Author:
Beth Harris
Steven Zucker
Date Added:
07/07/2021
Apollonius, Boxer at Rest, c. 100 B.C.E.
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This art history video discussion examines Apollonius' "Boxer at Rest", c. 100 B.C.E., bronze, Palazzo Massimo, Museo Nazionale Romano, Rome.

Subject:
Arts and Humanities
Art History
Material Type:
Diagram/Illustration
Lecture
Provider:
Khan Academy
Provider Set:
Smarthistory
Author:
Beth Harris
Steven Zucker
Valentina Follo
Date Added:
07/07/2021
Arch of Titus
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CC BY-NC-SA
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This art history video discussion examines the Arch of Titus, originally Pentelic marble, early 19h-century restoration is in travertine, c. 81 C.E. (Via Sacra, Rome).

Subject:
Architecture and Design
Arts and Humanities
Art History
Material Type:
Diagram/Illustration
Lecture
Provider:
Khan Academy
Provider Set:
Smarthistory
Author:
Beth Harris
Steven Zucker
Date Added:
07/07/2021
Arithmetic: More Long Division and Remainder Examples (Part 3 of 4)
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This arithmetic lesson demonstrates more long division problems with remainders.[Arithmetic playlist: Lesson 26 of 38]

Subject:
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
07/07/2021