Input (grade 13): A rotation of the orthonormal basis in terms of which vector is represented is obtained with a multiplication of by a rotation matrix. This matrix multiplication is just a compact representation of a sequence of dot products.
Output (grade 12): A rotation of the orthonormal basis in terms of which vector a is represented is obtained with a multiplication of a by a rotation matrix R/O. This matrix multiplication is just a compact representation of a sequence of dot products.