answer:We first find the horizontal component of the force: {eq}F_x = F cos theta = F cos 30^circ{/eq} The work done by this force is: {eq}W = F_x cdot x = (F cos 30^circ) (5.0) = 2.5 F sqrt{3}{/eq} Using the work-energy theorem, we have: {eq}begin{align*} W &= Delta KE 2.5 F sqrt{3} &= frac{1}{2} m v_f^2 - frac{1}{2} m v_i^2 2.5 F sqrt{3} &= frac{1}{2} (65) (4.0)^2 - 0 F &= frac{520}{2.5 sqrt{3}} F &approx boxed{120 , N} end{align*}[/eq] Therefore, the magnitude of the force applied by the rope is approximately 120 N.

answer:The stress tensor is a mathematical tool used to describe the internal forces acting within a continuous material. It is defined at each point within the material and provides information about the forces acting on an imaginary cut surface passing through that point. The face of the cut surface is significant because it determines the direction of the force being considered. For example, the stress tensor component T_{xx} represents the force acting in the negative x direction on a surface perpendicular to the x axis, while T_{zx} represents the force acting in the negative x direction on a surface perpendicular to the z axis. This distinction is important because it allows us to describe the forces acting on a material from different perspectives and to understand how these forces contribute to the overall stress state of the material.

answer:The term that best fits this description is "reluctant," as it indicates someone who goes along with political correctness unwillingly, just to avoid conflict or for social acceptance.

answer:The mode is the value that appears most frequently in a dataset. In this case, the value frac{17}{sqrt{pi }} appears four times, while all other values appear at most twice. Therefore, the mode of the given set of numbers is frac{17}{sqrt{pi }}. The answer is frac{17}{sqrt{pi }}