In a scaling transformation with factor 3 about the origin, each coordinate is multiplied by 3. So the point (2, -4) maps to (3·2, 3·(-4)) = (6, -12). The other options don’t come from a uniform scale by 3: staying the same would need a scale factor of 1; (3, -8) would require multiplying x and y by different amounts; and (0, 0) would require the original point to be at the origin or the scale factor to be 0.

Work in a fluid-piston system comes from the force the fluid pressure exerts over the piston and the distance the piston moves. The fluid pushes with a force F equal to pressure times the piston area, F = P × A. If the piston moves a small distance dx, the infinitesimal work is dW = F dx = P A dx. For a finite movement x at constant pressure, W = P A x. Since the change in volume is ΔV = A x, this is equivalent to W = P ΔV, and in general W = ∫ P dV when pressure varies. So the expression that matches this setup is pressure times piston area times the displacement, because it directly multiplies the pressure (the driving force per unit area) by the area to get force and by the distance the piston travels to get work. The units also work out to joules: Pa × m^2 × m = N/m^2 × m^2 × m = N·m = J. Other options don’t describe the work produced by the fluid on the piston in this context: density × height × velocity doesn’t yield the correct form or units for work; mass × gravity gives weight, not work; and while work is generally force × distance, that form doesn’t express the specific force from fluid pressure on the piston.

Momentum is defined as the product of an object's mass and its velocity, p = m v. This means how much motion an object has depends on both how heavy it is and how fast it’s moving. It’s a vector, so it points in the same direction as the velocity, and its units are kilograms times meters per second (kg·m/s). For example, a 5 kg object moving at 2 m/s has momentum 10 kg·m/s. The other expressions don’t describe momentum: distance times velocity mixes spatial and motion without capturing inertia; mass divided by velocity changes the quantity’s units and meaning; velocity times acceleration relates to something else (in certain contexts linked to power, not momentum).

Speed tells how far you go each hour, so time is found by rearranging the relation speed = distance / time into time = distance / speed. This expression directly computes how long a trip takes when you know how far you’re going and how fast you’ll go. For example, 120 miles at 60 miles per hour takes 120 / 60 = 2 hours. The units line up: miles divided by (miles per hour) leaves hours, which is the measure of time. The other forms don’t fit because they mix or invert the quantities improperly: multiplying distance by speed doesn’t produce a time, dividing distance by distance isn’t time, and adding distance and speed combines unlike quantities.