Every day we experiment motion and shape change of continuum media, assembly of different space dimension structures, fluids, solids which exhibit numerous evolutions either particular or general: large deformations, incompressibility, cavitation, contact, surface tension, defects, dislocations,... Stretch and rotation are a common feature of these motions and phenomenons. We base a continuum mechanics predictive theory on stretch and rotation quantified by matrices. In the Conclusion, the main results are emphasized: the choice of stretch matrix and rotation matrix as the base of the theory, the third gradient theory; the convexity of the free energy even in large deformation theory, this convexity being a physical property; the compatibility conditions which are conditionally satisfied by the stretch and angular velocities with conditions depending on the intensity of an internal stress accounting for the defects and dislocations which are quantified by a matrix.