The blocks are forced together, compressing a spring between them by a distance x; (the force constant of the spring is k) then the system is released from rest on a level, frictionless surface. The spring, which has negligible mass, is not fastened to either block and drops to the surface after it has expanded. What is the speed that block A acquired, vA

   v =    x

Explanation:

For this exercise let's use the important topic of conservation of energy

starting point. Spring compression point

          Em₀ = K_e = ½ k x²

final point. When the spring is not compressed

          Em_f = K = ½ m v²

as they indicate that there is no friction, the energy is conserved

          Em₀ = Em_f

          ½ k x² = ½ m v²

          v =    x

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.

in simple terms, the principle states that the buoyancy force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational acceleration, g. this is also known as upthrust.