Graphics libraries compose a rotation and a translation by multiplying their matrices, then apply the single product to every vertex. Why is that faster than applying the two transformations in turn?

A. Because the product is computed once and applied to every vertex.

Two transformations applied separately cost two matrix-vector multiplies per vertex, so a million vertices cost two million; composing first costs one small matrix-matrix product, once. That is why the model-view-projection matrix exists. The results are identical because multiplication is composition, what matters is order, which is the source of a great many graphics bugs.