The expression that indicates the amount of water, in gallons, in the swimming pool after \( m \) minutes can be found by adding the initial amount of water to the amount of water being added over time.
Since there are already 1,200 gallons of water in the pool and water is being added at a rate of 20 gallons per minute, the total amount of water after \( m \) minutes would be:
\[ 1,200 + (20 \times m) \]
So, the correct answer is:
A. \(1,200 + 20 \times m\).