What is the order of rotational symmetry for a square and an equilateral triangle?

Here's the order of rotational symmetry for each shape:

i) Square
A square can be rotated by $90^\circ$, $180^\circ$, and $270^\circ$ and still look the same as its original position. Including the $360^\circ$ rotation (which brings it back to the exact starting point), there are 4 such positions.
The order of rotational symmetry for a square is $\boxed{4}$.

ii) Equilateral triangle
An equilateral triangle can be rotated by $120^\circ$ and $240^\circ$ and still look the same as its original position. Including the $360^\circ$ rotation, there are 3 such positions.
The order of rotational symmetry for an equilateral triangle is $\boxed{3}$.