The onset of a vortex penetration into a hard isotropic superconductor after the rotation of an applied magnetic field (H) over right arrow is theoretically studied. On the basis of the Gibbs formalism, macroscopic equations describing this process are derived. Different magnetic prehistories are considered. It is shown that vortices entering into a sample are not parallel to the direction of (H) over right arrow. The angle between the vortices and (H) over right arrow can be unexpectedly large and reach pi/2.