Elastic and inelastic scattering of positrons by atoms and molecules are studied experimentally in a new range of positron energies, using a novel technique involving a magnetized beam of cold positrons. Differential cross-section measurements are presented for Ar and Kr at energies from 0.4 to 2.0 eV, and they compare well with theoretical predictions. The first low-energy measurements of the vibrational excitation of molecules by positrons is presented (i.e., CF 4 at energies from 0.2 to 1 eV), and comparison with electron scattering data is discussed. [S0031-9007 (99)09412-0] PACS numbers: 34.85. + x, 34.50.Ez, 41.75.Fr 5032 0031-9007͞99͞82(25)͞5032(4)$15.00