Consider two vectors P⃗ =7.5i^ and Q⃗ =−1.5i^+6.0j^. If another vector R⃗ =P⃗ +Q⃗ , what is the magnitude of R⃗ ?

If you were to drop a rock from a tall building, assuming that it had not yet hit the ground, and neglecting air resistance. what is its vertical displacement (in m) after 6 s?

Agraduated cylinder contains 63.0 ml of water. a piece of gold, which has a density of 19.3 g/ cm3, is added to the water and the volume goes up to 64.5 ml. calculate the mass in grams of the gold that was added to the water. explain how you got your answer.

Acarpenter builds an exterior house wall with a layer of wood 2.9 cm thick on the outside and a layer of styrofoam insulation 2.3 cm thick on the inside wall surface. the wood has k=0.080w/(m⋅k), and the styrofoam has k= 0.010 w/(m⋅k). the interior surface temperature is 19.0 ∘c , and the exterior surface temperature is -15.0 ∘c . a.)what is the temperature at the plane where the wood meets the styrofoam? celsius b.)what is the rate of heat flow per square meter through this wall? /m^2