Finding the Matrix of a Transformation Worksheet with Answer Key

What's on the worksheet

1. Write the rotation matrix R_θ with exact entries for each angle.
2. Zoe is animating a game sprite, a triangle pinned at the origin with its other two corners at A = (-4√(2), -2√(2)) and B = (-4√(2), 2√(2)).
3. Let L be the line through the origin in the direction d = (1, -4), and let P be the projection onto L.
4. Let F be the reflection of the plane across the line y = -2x.
5. Turns of R³ about the coordinate axes follow the right-hand rule.
6. Decide which of these matrices is a rotation, a reflection across a line, a projection onto a line, or none of these.
7. Let L be a line through the origin with unit direction u, and let P be the projection onto L, so Px = (x · u)\,u.