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Computing

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

Test Bank for Chemistry

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July 19, 2009 [PROBLEM SET FROM R. CHANG TEST BANK] w w w . k a u . e d u . s a / a a s i r i 2 Page 1 Chapter 7 Quantum Theory and the Electronic Structure of Atoms Student: _____________________________________________________________________ 1. What is the wavelength of radiation that has a frequency of 6.912 ? 1014 s-1? A. 1.447 ? 10-15 nm B. 4.337 ? 102 nm C. 2.304 ? 106 nm D. 2.074 ? 1023 nm E. 4.337 ? 10-7 nm 2. What is the wavelength of radiation that has a frequency of 2.10 ? 1014 s-1? A. 6.30 ? 1022 m B. 7.00 ? 102 nm C. 7.00 ? 105 m D. 1.43 ? 10-6 m E. 3.00 ? 108 m 3. Calculate the frequency of visible light having a wavelength of 486 nm. A. 2.06 ? 1014 /s B. 2.06 ? 106 /s C. 6.17 ? 1014 /s D. 1.20 ? 10-15 /s

Java Overview

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The core Java platform is the Java 2 Platform, Standard Edition or J2SE. At the foundation of the J2SE Platform is the Java Runtime Environment (JRE). The JRE runs the applications and applets coded in Java on a variety of platforms The second major component of the J2SE is the Java 2 Software Development Kit (SDK). It contains the JRE along with several other tools for developing Java applications and other applets. These tools include the Java compiler and debugger. The first step in creating a Java application is writing the Java source code in a text editor. Before you run the Java program that you have created, you need to compile it. You can do this using any machine that has a Java compiler installed.

russia! In Bright COLORS!

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Revolution in Russia There are several Issues that lead to the end of the Russian Monarchy 1. Russia was a backwater nation in 1914 dominated by the wealthy with the vast majority living in poverty 2.WW1 had strained the resources of Russia. Additionally within 2 years of the start 2 million people had been lost. 3. The influence of Rasputin over the czar?s or tzar's family was not popular among the Russian people. The March Revolution By March 1917, disasters on the battlefield,food shortages and a lack of fuel led to the collapse of the Russian Monarchy. Following the abdication of the czar local governments took charge eventually giving way to Lenin and the Bolsheviks (russian Communists) Lenin and the Bolsheviks

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