"Smart" surfaces, also known as stimuli-responsive surfaces, can change their properties (e.g., wettability, adhesion, friction, elasticity, and biocompatibility) in response to external stimuli (e.g., temperature, pressure, light, solvent selectivity, ionic strength, type of salt, pH, applied electric field, etc.). In this work, we use self-consistent field (SCF) calculations to study the solvent-response of diblock copolymer (A-B) brushes grafted all by the A block on a planar substrate. In particular, we investigate in detail the effects of copolymer chain length, volume fraction of the A block, chain-grafting density and A-B incompatibility on the brush height and surface switchability (characterized by the difference in surface-layer composition when treated by different solvents). Such knowledge is useful in designing "smart" surfaces for their applications. We further study the application of other stimuli (e.g., the solution pH, ionic strength and applied electric field) in addition to solvent selectivity when one of the blocks is charged. Our results are in good agreement with recent experiments.