Video no 167
In this QGIS video, I demonstrate the Advanced Digitising Toolbar and the Panel too.
A single polygon is dragged to a new location and then again to a new location using set distance and set angle.
The same is done on multiple selected polygons.
The features are also scaled up/down
Single and multiple polygons are also rotated

Note that when you have a selection of features, whichever one you clicked on in that selection to start your rotation, move or scale is the one that the new dimensions will be applied to.