State whether the following statements are true or false:
$(a)$ Power is the vector product of force and velocity.
$(b)$ $1\,kg\,m = 9.8\,J$
$(c)$ When a teacher rubs a blackboard with a duster,they do no work.
$(d)$ Kinetic energy can be negative.

(A) False. Power is the scalar (dot) product of force and velocity,i.e.,$P = \vec{F} \cdot \vec{v}$.
$(b)$ True. This represents the work done by gravity on a $1\,kg$ mass falling through $1\,m$,where $W = mgh = 1 \times 9.8 \times 1 = 9.8\,J$.
$(c)$ False. The teacher applies a force to move the duster against friction,thus doing work.
$(d)$ False. Kinetic energy $K = \frac{1}{2}mv^2$ is always non-negative because mass $m > 0$ and $v^2 \geq 0$.