VLT multi-object spectroscopy of 33 eclipsing binaries in the Small Magellanic Cloud New distance and depth of the SMC, and a record-breaking apsidal motion

Aims. Our purpose is to provide reliable stellar parameters for a significant sample of eclipsing binaries, which are representative of a whole dwarf and metal-poor galaxy. We also aim at providing a new estimate of the mean distance to the SMC and of its depth along the line of sight for the observed field of view.