Final answer:
The task involves using rotation matrices to find the new vector matrices after rotating an initial 2D vector by various angles.
Step-by-step explanation:
The question is related to vector rotation in mathematics, specifically in the context of finding the resulting matrices after rotating a vector by various angles. When a vector, represented here as a matrix, is rotated, we can use rotation matrices to calculate its new position. A rotation matrix for a counterclockwise rotation by angle θ is given by:
R(θ) = [cos(θ) -sin(θ)]
[sin(θ) cos(θ)]
Thus, to match the angles of rotation with the produced vector matrices, we must apply this rotation matrix to the initial vector matrix [-3 -5]. The resulting matrices can be found by matrix multiplication of the rotation matrix and the original vector matrix for the specified rotation angles.