A vector has components x = - 2 m and y = - 2 m. what is its direction (angle with respect to east) ?

Since both components are negative, so the vector lies on the 3rd quadrant.

Calculate for angle using tanθ:

tanθ = y / x

θ = tan^-1 (-2 / - 2)

θ = 45°

Since this is in 3rd quadrant, therefore when reference with respect to east or 1st quadrant, the angle is:

θ = 180 + 45 = 225° from the east (counter clockwise)

θ = 90 + 45 = 135° from the east (clockwise)