Precalculus, Chapter 6, 6.4, Section 6.4, Problem 34

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 = 2*1 + (-3)*(-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(2^2 + (-3)^2) =>|u|= sqrt 13
|v|= sqrt(v_x^2 + v_y^2) => |v|= sqrt(1^2 + (-2)^2) => |v|= sqrt 5
cos theta = (8)/(sqrt(13*5)) => cos theta = (8)/(sqrt 65)
Hence, the cosine of the angle between the vectors u and v is cos theta = (8)/(sqrt 65) , so, theta ~~ 7º 15' 8.089".