Precalculus, Chapter 6, 6.4, Section 6.4, Problem 33

You need to use the formula of dot product to find the angle between two vectors, u = u_x*i + u_y*j, v = v_x*i + v_y*j , such that:
u*v = |u|*|v|*cos(theta)
The angle between the vectors u and v is theta.
cos theta = (u*v)/(|u|*|v|)
First, you need to evaluate the product of the vectors u and v, such that:
u*v = u_x*v_x + u_y*v_y
u*v = 3*0 + 4*(-2)
u*v = -8
You need to evaluate the magnitudes |u| and |v|, such that:
|u|= sqrt(u_x^2 + u_y^2) => |u|= sqrt(3^2 + 4^2) =>|u|= 5
|v|= sqrt(v_x^2 + v_y^2) => |v|= sqrt(0^2 + (-2)^2) => |v|= 2
cos theta = (-8)/(2*5) => cos theta = (-4)/(5)
Hence, the cosine of the angle between the vectors u and v is cos theta = -4/5 , so, theta ~~ 143^o.