Find the a unit vector perpendicular to the surface
Z=x^2+y^2-z
at (1 ,2,3)

Asubmarine has a "crush depth" (that is, the depth at which water pressure will crush the submarine) of 250 m. what is the approximate pressure (water plus atmospheric) at this depth? (recall that the density of seawater is 1025 kg/m3, g = 9.81 m/s2, and 1 kg/(ms2) = 1 pa = 9.8692 10-6 atm.) a. 34.8 atm b. 24.8 atm c. 25.8 atm d. 7.8 atm

Samir watches a 100-minute movie on his spaceship. maria's spaceshipe flies in the same direction as samir's spaceship but she observes his move to last 125 minutes and his spaceship to be 40 m long. how long does samir observe his own spaceship to be? according to an observer on earth, planet x is stationary. maria and samir depart earth on their spaceships at the same time, each flying at 0.5c. maria flies toward planet x and samir flies in the opposite direction. according to maria, her voyage to planet x takes 9 years. how many years does marias voyage take according to samir?

Nacidified solution was electrolyzed using copper electrodes. a constant current of 1.18 a caused the anode to lose 0.584 g after 1.52 ✕ 103 s. given that the charge of an electron is 1.6022 ✕ 10−19 c, calculate avogadro's number. assume that copper is oxidized to cu2+ ions.