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

Scientists use laser range-finding to measure the distance to the moon with great accuracy. a brief laser pulse is fired at the moon, then the time interval is measured until the "echo" is seen by a telescope. a laser beam spreads out as it travels because it diffracts through a circular exit as it leaves the laser. in order for the reflected light to be bright enough to detect, the laser spot on the moon must be no more than 1.0 km in diameter. staying within this diameter is accomplished by using a special large-diameter laser. part a if λ = 540nm , what is the minimum diameter of the circular opening from which the laser beam emerges? the earth-moon distance is 384,000 km. express your answer to two significant figures and include the appropriate units.

The material that keeps its new shape after it is stretched is called?

This punnett square shows the cross between two pants. one parent has round seeds (rr). and the other parent has wrinkled seeds (rr) which best describes their offspring as shown in this cross?