Find the orthogonal projection of v onto the subspace w spanned by the vectors ui. (you may assume that the vectors ui are orthogonal.) v = 6 −3 9 −6 , u1 = 1 1 0 0 , u2 = 1 −1 −1 1 , "u3" = 0 0 1 1

Air is held within a frictionless piston-cylinder container, which is oriented vertically. the mass of the piston is 0.45 kg and the cross-sectional area is 0.0030 m2. initially (state 1) the pressure of the gas is sufficient to support the weight of the piston as well as the force exerted by the atmospheric pressure ( 101.32 kpa). the volume occupied by the air within the cylinder in state 1 is 1.00 liter. one end of a spring (with spring constant k = 1000 n/m) is attached to the top of the piston, while the other end of the spring is attached to a stage that can move vertically. initially the spring is undeflected and therefore exerts no force. then the stage is then moved quasistatically downward a distance of 10.0 cm, at which point the system reaches state 2. the piston-cylinder is not insulated; rather it remains in diathermal contact with the surroundings, which are at a constant temperature of 300 k. what is the change of pressure within the container?

If the chemical properties of a substance remain unchanged and appearance or shape of a substance changes it is called a ?

Which of the following are appropriate acceleration units?