Final answer:
The rook is the chess piece that can move across the entire board in a straight line, making it the correct answer to the student's question.
Step-by-step explanation:
The chess piece that can move across the entire board in one move, but only in a straight line, is the rook. The rook is one of the powerful pieces in the game of chess, and it can move any number of squares along a rank or file, but it cannot leap over other pieces. Therefore, the correct answer to the student's question is a) Rook. Knowing how pieces move is crucial for strategizing in chess, and experienced players use this knowledge to their advantage to control the board and capture the opponent's pieces.