(a) View 13 is View 1 subject to the following five transformations: 1. Scale by a factor of in the x-direction, 2 in the y-direction, and in the z-direction. 2. Translate unit in the x-direction. 3. Rotate about the x-axis. 4. Rotate about the y-axis. 5. Rotate about the z-axis. Construct the five matrices , , , , and associated with these five transformations. (b) If P is the coordinate matrix of View 1 and is the coordinate matrix of View 13, express in terms of , , , , , and P. Ex-View 13 View 1 scaled, translated, and rotated (Exercise 4)

Chapter 1.2.19 Definitions: Revenue (R) : What You Earn Cost (C) : What You Pay Profit: Revenue - Cost P = R - C Example: A Newspaper company sells high quality stories at a quick pace. The fixed cost for the newspaper paper is $70. The price to print a story is $0.39 per copy. What is the cost function 70- fixed cost 0.39- Marginal Cost X- Variable Cost Forming the function- C(x) =70 + 0.39X Marginal Cost: The increase in cost to sell one more copy Say we are given Revenue: R(x) =0.49X What would be the profit function What would be your profit P(X) = 0.49X - (70 + 0.39X) Solve! P(X) = 0.49X - (70 + 0.39X) = 0.49X - 70 - 0.39X = 0.10X - 70 Say there are 500 copies, What is your profit or loss of profit 500 Copies P(x) = 0.10x - 70 = 0.10(500) - 70 = 50 - 70 = - 20 What is the Breakeven point ( what this means is we make the equation equal to zero) P(X) = 0.10X - 70 0=0.10X - 70 Add 70 on both sides 70 = 0.10x Divide both sides by 0.10 X = 700 Chapter 1.2.21 Example: Equation: C(X) = 1500 + 10X +0.2X^2 Say your Revenue is: R(X) = 105X Find the Price equation and solve: P(X) = 150X - (1500 +10X - 0.2X^2) = 105X - (1500 + 10x + 0.2X^2) = 105X - 1500 - 10x - 0.2X^2 = 95X - 1500 - 0.2 X^2 P(X) = - 0.2X^2 + 95X - 1500 (Parabola) What's the Breakeven point 0 = - 0.2X^2 +95x -1500