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A = 4 2
-5 -2
Find an invertible 2x2 matrix Q such that Q^-1AQ is equal to a rotation followed by scaling by a positive real number, and write down both the rotation matrix and the scaling matrix. What is the angle of rotation of the matrix?
How to make a rectangular berry tart th length of the tart has to be twice its width in a area of 72 square inches.What dimensions can be use to make a tart with an area of 72 square inches?
Water waves in a lake travel 4.73 m in 1.01 s. The period of oscillation is 1 s. What is the speed of the water waves? Answer in units of m/s.
The weight of water provided the force on the wheel to turn the axle. If the axle provides 3750N of force, and the effective weight of the water can provide a tangent force on the wheel of 325N, what is the minimum radius of the wheel if the axle radius is 55 cm.
If a small positive charge is brought near a large positively charged conductor, what happens to its electrical potential energy?
a. because the charges are the same the energy is reduced
b. because they repel, its potential energy will increase
c. because the charges are the same. the energy will not be changed
d. there is not enough information provided to determine
Electrical potential energy is the energy a charged object has due to its?
a. movement in an electrical field
b. energy
c. position in an electric field
d. height off the ground
A 5-C charge is located near a positively charged sphere so that it has 50 J of electric potential energy. Its electric potential is what?
a. 2 V.
b. 5 V.
c. 10 V.
d. 20 V.
Electric potential is defined as
a. electrical potential energy of a charge multiplied by the charge
b. electrical potential energy of a charge divided by the quantity of the charge
c. electrical potential energy
d. voltage
Earthquakes produce two kinds of seismic
waves: he longitudinal primary waves (called
P waves) and the transverse secondary waves
(called S waves). Both S waves and P waves
travel through Earth’s crust and mantle, but
at different speeds; the P waves are always
faster than the S waves, but their exact speeds
depend on depth and location. For the pur-
pose of this exercise, we assume the P wave’s
speed to be 9620 m/s while the S waves travel
at a slower speed of 5990 m/s.
If a seismic station detects a P wave and
then 31.6 s later detects an S wave, how far
away is the earthquake center?
Answer in units of km.
The highest recorded temperature on Krypton was 142 degrees F. The lowest recorded tempera-
ture was −93 degrees F.
Express the low temperature extreme in degrees Celsius.
Answer in units of degrees C.
