Problem 1 (Adding to a vector) Suppose that you have a vector v1=(x,y), and a second vector v2=(x2,y2). Neither vectors are normalized. 1. How do you calculate sum of the two vectors? 2. Suppose you wanted to add a vector that is twice the magnitude of v2 to v1, how would you do that? 3. How do you increase v1 by the magnitude of v2 but without altering the direction of v1?

Problem 2 (rotating a vector) Suppose you were given a vector and an angle in degrees. A positive angle represents a counter-clockwise rotation while a negative angle represents a clockwise rotation. How do you calculate a new vector that represents a rotation of the original vector by the indicated angle?