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city-State key term card

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-early complex political unit made up of an urban area and its surrounding farmland, usually surrounded by protective walls. -starting in the neolithic age through the classical period in the mediterranean region(mid east, W. europe, N. africa) --first complex governments that developed with the rise of civilizations. --developed out of need for organization and protection --high walls show that wars for land resulted from the development of agriculture

Dot Product (and Vector Projection)

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Vector Algebra ? Vector Addition ? Scalar Multiplication ? How about the product of two vectors? 1. Dot Product ?v ? ?u 2. Cross Product ?v ? ?u Dot Product Take 3-D for example, De?nition If two vectors ?a =< a 1 , a 2 , a 3 > and ?b =< b 1 , b 2 , b 3 >, then the dot product (inner product, scalar product) of ?a and ?b is de?ned as ? a ? ? b = a 1 b 1 + a 2 b 2 + a 3 b 3 Example < 2,?4 > ? < 3, 5 > = ?14 (?i + 2?j ? 4?k) ? (?2?i +?j + 3?k) = ?12 Remark: Dot product gives a scalar. Properties: 1. ?a ??a = a2 1 + a2 2 + a2 3 = |?a|2 2. ?a ? ?b = a 1 b 1 + a 2 b 2 + a 3 b 3 = ?b ??a 3. ?a ? (?b + ?c) = ?a ? ?b +?a ? ?c 4. (c?a) ? ?b = c(a 1 b 1 + a 2 b 2 + a 3 b 3 ) = c(?a ? ?b) = ?a ? (c?b) 5. ?0 ??a = 0

vocab chapter 8

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Second Continental Congress The Second Continental Congress met in Philadelphia on May 10, 1775. Three delegates added to the Congress were Benjamin Franklin, Thomas Jefferson, and John Hancock. The Congress took on governmental duties. (United all the colonies for the war effort.) They selected George Washington as Commander in Chief. They encouraged the colonies to set themselves up as states. On July 4, 1776 they adopted the Declaration of Independence. The Congress ended March 1, 1781 when a Congress authorized by the Articles of Confederation took over. Ethan Allen Led a tiny American force and captured fort Ticonderoga and Crown Point on the scenic lakes of upper New York Benedict Arnold

Chapter 5 Summary American Pageant 13th

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Chapter 5 Info Sheet People- Dr. Samuel Jackson Thomas Jefferson Jonathon Edwards George Whitefield Benjamin Franklin John Trumbull Benjamin West Singleton Copley Phillis Wheatley Events- The march of the Paxton Boys (1764) Postal system mid-1700s The Great Awakening- stage of rousing religious revival Wars/Conflicts- Reasons for rebellion of the 13 colonies were population growth, American colonists were out numbered by English Crisis/Panics- Colonists were afraid of black slave rebellion Land/Territorial Acquisitions- Roads were scarce Foreign Policy- Triangle trade Arts/Literature/Education- College of William and Mary established in 1693 Offered education to all types of people Religion- Anglican Congregational

Chapter 4 Summary American Pageant 13th

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Chapter 4 Info Sheet People Governor William Berkeley Nathaniel Bacon Conflicts/Wars- Bacon’s Rebellion- poor farmers vs. Berkley and Indians. Crisis/Panics- Disease in early English settlements making nuclear families hard to come by “Middle Passage” Slavery in the South Religious Happenings Half-way Covenant and the “jeremiad” Salem Witch Trials Land/Territorial Acquisitions- New England soil was rocky Settlers believed that purifying the soil by burning the forest was wasting the land. They took away the Indians land because they figured they didn’t want it because they burnt it. Documents- “Headright” System- whoever paid for an indentured servant got land “slave codes” Political Parties-

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