Assignment:
Assume the operator R(theta) transforms a vector v (in two-dimensional real space) by swinging it around counterclockwise through an angle theta. How can I show that the operator R(theta) has the matrix representation
cos(theta) -sin(theta)
sin(theta) cos(theta)
That is supposed to be a matrix.
Provide complete and step by step solution for the question and show calculations and use formulas.