Vectors Topic and contents Vectors Definition (Vectors in Rn ) For any positive integer n‚ a vector a ∈ Rn is an n-tuple of real numbers‚ that is an ordered list of n real numbers School of Mathematics and Statistics MATH1151 – Algebra (a1 ‚ a2 ‚ a3 ‚ . . . ‚ an−1 ‚ an ) Notation: a ∈ Rn ‚ vector a‚ by hand a ‚ ∈ is an element of ˜ n) Example (Vectors in R √ u = (1‚ 2)‚ v = (2‚ 1) ∈ R2 z = (0‚ π‚ 3.2‚ e‚ 2‚ 4) ∈ R6 A/Prof Rob Womersley ✞ Lecture ✝ 1 2 3 ☎ 01
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M13/5/MATME/SP1/ENG/TZ1/XX 22137303 mathematics STANDARD level Paper 1 Candidate session number 0 0 Thursday 9 May 2013 (afternoon) Examination code 2 1 hour 30 minutes 2 1 3 – 7 3 0 3 instructions to candidates Write your session number in the boxes above. not open this examination paper until instructed to do so. Do You are not permitted access to any calculator for this paper. Section A: answer all questions in the boxes provided
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Simplifying Expressions 2a(a-5)+4(a-5) The given expression. a*2 Multiply a and 2. 2a^2 2*a*2 = 2a^2. 2a^2*a-5 The distributive property removes the parenthesis. 2a × -5 = -10a Multiply 2a by -5=-10a. -10a 2a^2-10a + 4(a-5) Use the distributive property to remove the parentheses. 4*a= 4a 4*-5= -20 Multiply 4 by a-5. 4 × a = 4a 4*-5=-20 Multiply 4 by a‚ and 4 by -5 4a-20 2a^2-10a + 4a -20 Add the coefficients; combine like
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Learning Strategies Lesson Learning Strategies Lesson According to Dr. Deshler‚ most students begin to experience a performance gap in the fifth grade (Laureate Education‚ Inc.‚ 2012a). The bridge to close this gap is built by changing the pedagogy of the teacher and the learning strategies of the students. The learning strategies taught to the students enable them to develop into independent thinkers and learners (Friend & Bursuck‚ 2009). Student-centered learning incorporates effective
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The Study of Values by Frank Lynch The Filipino today‚ in his attempt to modernize and develop‚ faced with a two-fold endeavor: to strengthen his national identity and to cope with never-ending changes. Experience has taught us institution‚ systems‚ and values copied from Western models do not operate effectively in the Philippines as they do in their original setting. The Filipino himself is at loss because of the impact of several values‚ something conflicting ones‚ on his best in him to enable
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Different factors impact one’s decisions‚ possibly changing their lives permanently. In the memoir‚ The Other Wes Moore‚ both Wes Moore’s nature and how they were nurtured influenced their decisions‚ successes‚ and failures. Drugs in both Wes Moore’s environments have similar effects on their decisions‚ successes‚ and failures‚ as opposed to their role models‚ who had different effects on them. Environment plays a crucial role in one’s life. If someone was stuck in a bad environment‚ it would have
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Banana Pizza Ravioli Once upon a time there was a lady. She was a coloured lady‚ in a red jacket. The jacket probably came from a thrift store‚ because it wasn’t a very fancy jacket. The lady though‚ is the focal point of my story‚ more so than the jacket. This is my thesis statement. See‚ the lady was afraid of cameras. The flashes caused her pupils to dilate‚ her head to twitch‚ and her mind to explode… Well‚ the last one’s false‚ but it sounded like a decent additive to the story. So anyways
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Bryan Flores Ms. Riney 10/18/11 Movie Types There are lots of types of movie’s but do you know which one people like the most? There are three types of movie that are most popular among the general public: action‚ comedy and science fiction movies. All three movie types of have amazing movies they all have blockbuster hits. People always enjoy movies but there are 3 that people enjoy the most. When people go to a theater they always prefer a specific movie type over another.
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Detailed Lesson Plan in Mathematics IV (Review Lesson) I. Objectives: During the review activities‚ pupils are expected to: a. Identify the different properties of multiplication; b. explain the importance of cooperation; c. answer the challenge/exercises about the properties of multiplication Value Focus: Cooperation II. Subject Matter: Properties of Multiplication Reference: Math for all IV. Pages 111-113
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Module 4 Single-phase AC Circuits Version 2 EE IIT‚ Kharagpur Lesson 13 Representation of Sinusoidal Signal by a Phasor and Solution of Current in R-L-C Series Circuits Version 2 EE IIT‚ Kharagpur In the last lesson‚ two points were described: 1. How a sinusoidal voltage waveform (ac) is generated? 2. How the average and rms values of the periodic voltage or current waveforms‚ are computed? Some examples are also described there. In this lesson‚ the representation of sinusoidal (ac) voltage/current
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