Fill the shape with all the pieces. Drag a piece onto the shape and it clicks in where it fits. Tap a piece to turn it. Rotate and ⇄ Flip act on the last piece you touched, wherever it is lying. Pieces can rest anywhere.
Puzzle 1 is the seven classic pieces — only the parallelogram is ever changed by a flip. A piece sits anywhere it fits the shape exactly, in steps of half a cell. Puzzle 2 opens once it is done: the same shape, cut into nine pieces of its own for the day, and any of them may need flipping.
Keys: R rotates, F flips. Without a mouse: Tab to a piece, Enter to take it, arrows to move it, Esc to let go.