Given a point p = (3, 1, 2) and using the homogenous representation:

(a) calculate the coordinates of the transformed point p* if p is rotated about the x, y, and z axes by angles 60°, 30°, and 60° respectively.
(b) if the point p* obtained in part (a) is to be rotated back to its original position, find the corresponding rotation matrix. verify your answer.
(c) calculate p* if p is translated by d = 2i – 3j + k and then scaled uniformly by s=3.0.

Aswimming pool had 2.5 million liters of water in it. some water evaporated, and then the pool only had 22 million liters of water in it. what percent of the water evaporated?

The weekly revenue for a company is r = 3p^2 + 60p + 1060, where p is the price of the company's product. what price will result in a revenue of $1200.

The cross-sectional areas of a right triangular prism and a right cylinder are congruent. the right triangular prism has a height of 6 units, and the right cylinder has a height of 6 units. which conclusion can be made from the given information? the volume of the triangular prism is half the volume of the cylinder. the volume of the triangular prism is twice the volume of the cylinder. the volume of the triangular prism is equal to the volume of the cylinder. the volume of the triangular prism is not equal to the volume of the cylinder.