Hi, I need help on problem 5 and 6. Please explain it thoroughly as well as I am trying to understand it.

Problem 5 (rotating in vector) (3 marks} Suppose you were given a vector and an angle in degrees. A positive angle represents a counter-clockwise rotation while a negative angle represent: a clockwise rotation. How do you calculate a new vector that represents a rotation of the original vector by the indicated angle? Problem 6 {Calculating a reection vector} {9 marks) Suppose you were given a vector v:[x,y]. suppose that v describes the velocity of an object hitting a surface, who's normal [a unit vector that is 90 degrees from the surface is described by a unit vector). How would you nd the reflection vector (r) which is a vector that reflects v on the surface where the angle of reflection it the angle of incidence is the same as the angle of reection? [see diagram below} Your solution must work for surfac that are horizontal or vertical. Ideally it will work for surfaces that are slanted. r; uracc in the above diagram: I v {purple} is the vector representing the velocity of the object hitting a surface. I n {green} is the normal, a unit vector perpendicular to the surface in the direction of the space I r [light blue) is the result, which is a vector that reflects off the surface. note the same angle exists between the normal and the r and v