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1. If P(x, y, z) is any point on the surface of a sphere centered at (2, 3, 4), obtain the equation of the sphere using vectors.
2. Given A = a x cos α + a y sin α, B = a x cos β - a y sin β, and C =a x cos β + a y sin β, show that each is a unit vector. If β α, sketch these vectors and show that they are coplanar. Using these vectors ob- tain the following trigonometric identities: sin(α + β) = sin α cos β + cos α sin β, and sin(α - β) = sin α cos β - cos α sin β.
A microwave oven operates at 2.7 GHz. Evaluate what is the distance between wave crests in the oven
A water storage is filled with freshwater to a depth of 6.4m. It has a circular basin with an Area of 30m^2, What is the weight (force) of the water the basin supports
A proton is fired directly into a uniform electric field that is able to bring the charge momen- tarily to rest. How much work does the electric field do in stopping the proton
A double convex lens has faces of radii 18.0 cm and 20.0 cm. When an object is placed 24.0 cm from the lens, Determine the focal length of the lens
two resistors have resistances rsmaller and rlarger where rsmaller lt rlarger. when the resistors are connected in
A geologist finds that a moon rock whose mass is 8.08 kilogram has an apparent mass of 5.12 kilogram when submerged in water. Evaluate what is the density of the rock
A 0.240 kg block on a vertical spring with spring constant of 4.20 103 N/m is pushed downward, compressing the spring 0.045 m. How high does it rise above the point of release
An electric heater is constructed by applying a potential difference of 110 V across a wire with a resistance of 5.0 W
10.0 moles of an ideal gas, at an initial pressure of 1.50 x105 N/m2 and an initial volume of 1.300 m3, Find the work done by the gas
Ship moving initially at 10.7 m/s due North, drifts due NE at the same speed. To correct the bearing, the captain accelerates the engine and turns the rudder NW. If the engines deliver a constant acceleration of 4.4 m/s2, how long will it take to a..
What is the radius of curvature of the mirror. How far would it coast before starting to roll back down.
What is tension in each string
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