A stainless steel member has a three-dimensional state of stress at a critical location where sx = 50,000, sy = –10,000, sz = 15,000. txy = –3500, tyz = –1000, and tzx = 2000 psi. Calculate the first, second, and third stress invariants and solve the characteristic equation for the principal normal stresses. Also, calculate the maximum shear stress and draw the Mohr circle representation of the state of stress at the critical point.

Magma  is composed of molten rock and is  stored  in the earth's crust. lava is  magma  that reaches the surface of our planet through a volcano vent.

The boat's velocity relative to the riverbank can be resolved into two components. the component going north is 2.7 m/s and the component going west is 1.2 m/s.we add these two vectors and then find the magnitude of the resultant to get the speed.the magnitude of the resultant vector from adding can be obtained by the pythagorean theorem.    to two significant figures, the boat's speed relative to the riverbank is 3.0 m/s.

The figure is missing but we can answer anyway.the correct answer is "releasing the string". in fact, when the person is holding the bow and the arrow, the kinetic energy of the arrow is still zero (because the arrow is not moving). the moment the arrow is released, it acquires a velocity v, so its kinetic energy will become different from zero: where m is the mass of the arrow and v its velocity.  all the other options, instead, do not increase the kinetic energy of the system: -  pulling farther back on the string : this will just increase the elastic potential energy of the system-  holding the arrow higher: this will increase the gravitational potential energy of the system (which is given by u=mgh, where h is the height above the ground)-  decreasing the mass of the arrow: this will decrease the gravitational potential energy of the system (which is given by u=mgh, where m is the mass)