Apilot flies her route in two straight-line segments. the displacement vector a for the first segment has a magnitude of 260 km and a direction 30.0o north of east. the displacement vector b for the second segment has a magnitude of 176 km and a direction due west. the resultant displacement vector is r = a + b and makes an angle θ with the direction due east. using the component method, find (a) the magnitude of r and (b) the directional angle θ.

The scalar triple product computes the magnitude m of the moment of a force vector f about a specified line. it is m = (r × f) · n, where r is the position vector from the line to the point of application of the force and n is a unit vector in the direction of the line. use matlab to compute the magnitude m for the case where f = [12, −5, 4] n, r = [−3, 5, 2] m, and n = [6, 5, −7].

Acarpenter builds an exterior house wall with a layer of wood 2.9 cm thick on the outside and a layer of styrofoam insulation 2.3 cm thick on the inside wall surface. the wood has k=0.080w/(m⋅k), and the styrofoam has k= 0.010 w/(m⋅k). the interior surface temperature is 19.0 ∘c , and the exterior surface temperature is -15.0 ∘c . a.)what is the temperature at the plane where the wood meets the styrofoam? celsius b.)what is the rate of heat flow per square meter through this wall? /m^2

How many neutrons does element x if it’s atomic number is 28 and its mass number is 87