A good answer might be:

Plugging the numbers into the MS Windows calculator:

arc tan( y/x ) = arc tan( -4/3 ) = arc tan( -1.333333333333 ) =  -53.13^o

More Meddlesome Minuses

The calculation looks about right, in the diagram. If you want the angle to be expressed as a counter-clockwise rotation, then it is 360^o - 53.130^o = 306.870^o

Sadly, it looks like the vector -p will give you the same result. So what to do? Always sketch the vector when you are computing its orientation. Then you can see that the angle you want for -p is 180^o - 53.130^o = 126.87.

QUESTION 5:

What is the orientation of u = (-4, -2)^T ? (Sketch the vector first, then use a calculator.)