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Let D4 be the group of symmetries of the square That is, D4 = {1, R,...
Let Ds be the group of symmetries of the square. (a) Show that Ds can be generated by the rotation through 90° and any one of the four reflections. (b) Show that Dg can be generated by two reflections. (c) Is it true that any choice of a pair of (distinct) reflections is a generating set of Dg?
ANSWER 2 & 3 please. Show work for my understanding and upvote. THANK YOU!! 2. Given a regular n-gon, let r be a rotation of it by 2π/n radians. This time, assume that we are not allowed to flip over the n-gon. These n actions form a group denotecd (a) Draw a Cayley diagram for Cn for n-4, n-5, and n-6 (b) For n 4, 5, 6, find all minimal generating sets of C.· [Note: There are minimal generating sets...
3. Let T : R2 + Rº be the rotation by 1/2 clockwise about the origin, and let S : R2 + R2 be the shear along the y-axis given by S(x,y) = (x,x+y). (You may assume that these are linear transformations.) (a) Write down, or compute, the standard matrix representations of T and S. (b) Use (a) to find the standard matrix representations of (i) SoT (T followed by S), and (ii) ToS (S followed by T). (c) Let...
GEOMETRY Exam 9-Continued Student Number Student's Name 17. The vertices of AABC are A(-1, 1), B(0, 3), and C(3,4). Graph the image of AABC after a composition of the following transformations in the order they are listed. B A. Translation: (x. y)(x-3,y- 3) Reflection: in the line y x Is the composition a glide reflection? Yes No Yes Is the image the same if the order of the transformations is switched? (reflection, then glide) No 18. The vertices of AABC...
please do the number 2 1. Construct affine linear transformations to do the following to the square in Figure 4.la (a) Rotate the square 180° counterclockwise around the origin (in the plane) width. unchanged) (b) Move the square 7 units to the right, 3 units up, and double its (c) Make the vertical lines of the square slant at a 45 angle (height (d) Reflect the square about the y-axis. u Au + b, giving A and b. 4.la for...
(1) Let F denote the inverse square vector field (axr, y, z) F= (Note that ||F 1/r2.) The domain of F is R3\{(0, 0, 0)} where r = the chain rule (a) Verify that Hint: first show that then use (b) Show that div(F 0. (c) Suppose that S is a closed surface in R3 that does not enclose the origin. Show that the flux of F through S is zero. Hint: since the interior of S does not contain...
Use the following information To help you solve the following questions. Show all work for thumbs up. 3.1 Rotations and Angular-Momentum Commutation Relations 159 We are particularly interested in an infinitesimal form of Ry: (3.1.4) where terms of order & and higher are ignored. Likewise, we have R0= ° :- R(E) = 1 (3.1.5) and (3.1.5b) - E01 which may be read from (3.1.4) by cyclic permutations of x, y, zthat is, x y , y → 2,2 → x....
help on all please and thanks 6.2.1 Study: Paper Folding Liberal Arts Mathematics 1 Sem 2 Name Date Use the questions below to keep track of key concepts from activity this lesson's study 1) Practice: Organizing Information do constructions with paper folding, you need to know how to do the following and draw 1. Mark 2. Fold to make two things align and show they are 2) Practice: Summarizing In 10 words or less, define midpoint of a segment midpoint...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
B oth 100 Day PH262 Page 1 of 5 Lab #13 AC Circuits, Part 1 RC & RL, Phase Measurements THEORY The rotating phase representation for series AC circuits should be familiar from textbook and lecture notes A brief outline of the essential points is provided here. If a series RLC circuit is connected across a source of om which is a sinusoidal function of time, then und all its derivatives will also be inside. Sonce all demits in a...