PROBLEM 1 1.1 Let S CR2. Write down the definition of a symmetry of S. 1.2 Let G = Z/14Z. What is the order of the element [4] Є G? Does this element generate G? 1.3 What does it mean for a matrix A Є M₂(R) to be orthogonal? If A is orthogonal and det(A) = 1, what does A represent geometrically? No explanation is required. 1.4 Give an example of a subset SCR² for which the group E2(S, R) is finite but not abelian. No explanation is required.
PROBLEM 1 1.1 Let S CR2. Write down the definition of a symmetry of S. 1.2 Let G = Z/14Z. What is the order of the element [4] Є G? Does this element generate G? 1.3 What does it mean for a matrix A Є M₂(R) to be orthogonal? If A is orthogonal and det(A) = 1, what does A represent geometrically? No explanation is required. 1.4 Give an example of a subset SCR² for which the group E2(S, R) is finite but not abelian. No explanation is required.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 46E
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