5. I mentioned in class that rotation counter-clockwise by 0 radians is a linear transformation Re : R2 - R2. In this problem, you will find a formula for this linear transformation. a) Take the point in the plane (one unit right on the x-axis). Explain why rotating this point 0 radians counter-clockwise gives the point cos O sin 0 b) Take the point in the plane (one unit up on the y-axis). Explain why rotating this point 0 radians counter-clockwise gives the point (cos(0 + TT / 2) sin (0 + 7/2) Some high-school trig shows that this is equal to -sin (0) cos(0) c) In the previous two parts, you showed that cos 0 Re sin 0 Re sin 0 cos 0 Use the assumption that Re is linear to show that Re x cos 0 - y sin 0 x sin 0 + y cos 0