The angle through which the arrow rotates is the angle between the tangent vector evaluated at t=3 and t= 4. And you can find that from . Since these are unit tangent vectors, that is just .
A linear transformation in two dimensions can be represented as a two by two matrix. The linear transformation that maps to is the matrix, satisfying . That reduces to the two equatons and . Solve those equations for a, b, c, d (using your values for , of course).