If w is a subspace of r" and if is in both w and w, then must be the zero vector in the orthogonal decomposition theorem, each term in y is itself an orthogonal projection of f onto a subspace of w. lf у z1 +z2, where ź1 is in a subspace w and z2 is in w , then z1 must be the orthogonal projection of y onto w the best approximation to y by elements of a subspace w is given by the vector y-projwy. if an n p matrix u has orthonormal columns, then uutx= for all x in rn

If the wheels lock when braking suddenly the vehicle: a: loses traction b: lose steering wheel ability c: gain speed slightly d: gain steering ability

Clothing made of several thin layers of fabric with trapped air in between, often called ski clothing, is commonly used in cold climates because it is light, fashionable, and a very effective thermal insulator. so it is no surprise that such clothing has largely replaced thickand heavy old-fashioned coats. (a) consider a jacket made of five layers of 0.1-mm-thick synthetic fabric (k = 0.13 w/m·°c) with 1.5-mm-thick air space (k = 0.026 w/m·°c) between the layers. assuming the inner surface temperature of the jacket to be 28°c and the surface area to be 1.25 m2, determine the rate of heat loss through the jacket when the temperature of the outdoors is 0°c and the heat transfer coefficient at the outer surface is 25 w/m2·°c. (b) what would your response be if the jacket is made of a single layer of 0.5-mm-thick synthetic fabric? what should be the thickness of a wool fabric (k = 0.035 w/m·°c) if the person is to achieve the same level of thermal comfort wearing a thick wool coat instead of a five-layer ski jacket?

What is the average speed of a car that travels 40 mph for 1 hour and 60 mph in another hour?