Prove that the planar affine isometry represents a rotation through an angle of 90° around the center

Question:

Prove that the planar affine isometry

represents a rotation through an angle of 90° around the center (3/2, -1/2)T.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

See More Books

Question Posted: Jun 17, 2016 09:00 AM

See More Questions

In each case show that 7 is either reflection in a line or rotation through an angle, and find the line or angle. (a)
In each case show that that T is either projection on a line, reflection in a line, or rotation through an angle, and find the line or angle. (a) T[x y]T = 1/2[x - y y - x]T (b) T[x y]T = 1/5[-3x +...
Given data points (xo, uo). .........(xn un) with x, , i j, prove that there is a unique continuous piecewise affine interpolant u = f(x), so u = 0..........n. (a) Prove that the piecewise affine...
Considering these data where 'P1' estimates are analyst forecasts of future stock prices: Stock PO P1 A B C D B 52.5 59 0.4 1.1 24.5 29 0.26 2.1 36.4 43 0.23 1.5 38 42 0.33 1.4 Market Risk Premium...
The Swiss Credit Bank issued a letter of credit in favor of Antex Industries to cover the sale of 92,000 electronic integrated circuits manufactured by Electronic Arrays. The letter of credit...
The chief executive officer of Home Workout Equipment Corporation remarked to a colleague, I dont understand why other companies waste so much time in the budgeting process. I set our company goals,...
Refer to Exercise 4.107 and find E(x) = p. Then use the sampling distribution of i found in Exercise 4.107 to find the expected value of i. Note that E(7) = I*..
Wyrick Inc. had the following transactions pertaining to investments in common stock . Jan. 1 Purchased 2,500 shares of Murphy Corporation common stock (5%) for $140,000 cash plus $2,100 brokers...
Sales-Related Transactions, Including the Use of Credit Cards Journalize the entries for the following transactions: a. Sold merchandise for cash, $16,760. The cost of the merchandise sold was...
Ed is a professional photographer. He has been very successful over the years and has been retained to do professional advertising photo layouts for products like polo equipment, sports clothing, and...
Describe the image of (i) The x-axis (ii) The unit disk x2 + y2 ¤ 1 (iii) The unit square 0 ¤ x, y ¤ 1 under the following affine transformations: (a) Ti r) G) (3)
Prove that every proper affine plane isometry F[x] = Qx + b of R2, where det Q = 1, is either (a) A translation, or (b) A rotation (7.40) centered at some point c R2.
A horizontal structure consists of an L A = 10-mm-thick layer of copper and an L B = 10-mm-thick layer of aluminum. The bottom surface of the composite structure receives a heat flux of q" = 100 kW/m...
Air at $1 \mathrm{~atm}$ and $25^{\circ} \mathrm{C}$ flows in a 4-cm-diameter glass pipe at a velocity of $7 \mathrm{~m} / \mathrm{s}$. The friction factor for this flow is (a) 0.0266 (b)...
Find the regime of the boundary layer at the location of $0.1 \mathrm{~m}$ from the leading edge of an aerofoil, if the airspeed is $80 \mathrm{~ms}^{-1}$, and air condition is at that of sea...
``Nuclear Deterrence,'' by Harvey A . Smith, UMAP327. The author analyzes the stability of the arms race, assuming objectives similar to those suggested by General Taylor. The module develops...
A saturated vapor feed at $1000.0 \mathrm{kmol} / \mathrm{h}$ of methanol $(5.0 \mathrm{~mol} \%)$ and water $(95.0 \mathrm{~mol} \%)$ is fed to a distillation column with 18 stages plus a...
Use the partition functions in Equations 1.98, 1.99, and 1.100 to find the translational, rotational, and vibrational contributions to the average energy of a diatomic molecule. Compare each result...
State the third law of thermodynamics and explain its significance.
During registration at Tech every quarter, students in the Department of Management must have their courses approved by the departmental advisor. It takes the advisor an average of 4 minutes...
Consider the bottle wall thickness measurements described in Exercise 8-29. Compute a 90% prediction interval on the wall thickness of the next bottle tested.
How would you obtain a one-sided prediction bound on a future observation? Apply this procedure to obtain a 95% one-sided prediction bound on the wall thickness of the next bottle for the situation...
Consider the fuel rod enrichment data described in Exercise 8-30. Compute a 99% prediction interval on the enrichment of the next rod tested. Compare the length of the prediction interval with the...
On Dec 31 2020, Bernice Melson, a partner in ABC Communications, had an ending capital balance of $49,000. Her share of the partnership's profit was $18,000; she made investments of $12,000 and had...
Q2R. on account for each depreciable asset. During 2024, Jane VIIS nsactions.) i More Info Apr. 1 Purchased office equipment. 5111,000. Paid 581,000 cash and financed the remainder Jan. 1 with a note...
The rate of return on Cherry Jalopies, Inc., stock over the last five years was 14 percent, 11 percent, 4 percent, 3 percent, and 7 percent. What is the geometric return for Cherry Jalopies, Inc.?

Prove that the planar affine isometry represents a rotation through an angle of 90° around the center

Question:

x- 2

Step by Step Answer:

Write y Fx Qx a a where represents a rotation thro...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions