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1. Find the order of the group of transformations that leaves an equilateral triangle invariant. Identify the complete set of group elements, find a matrix representation, and then construct the multiplication table. What is the common name of this group?
2. Show that the two expressions below are equivalent.
What conditions are necessary for this equivalence?
3. Derive the position-momentum Heisenberg Uncertainty Principle. What is the value of ΔxΔpx for the Gaussian wave packet
Suppose the variance, cr2 is the complex number oi + io-?, then what is the value of axagis (be careful about normalization)? What is the solution to the Schrodinger equation of a free particle if 0(x) is taken as the initial condition 0(x, t = 0)?
4. For the wave function, ii)(x) = co exp(ipox/h)/1/42 + x2, find the normalization constant co and the probability of finding the particle in the interval ±a//5. What is the mean momentum?
What is the instantaneous power, at a time of 0.00700 seconds, dissipated by a 200 ohm resistor in a resonant AC circuit powered by a generator with a 21.0 V highest potential difference operating at 5000 rad/s .
A 2.1-kg block is released from rest and allowed to slide down a frictionless surface and into a spring. The far end of the spring is attached to a wall, as shown. The initial height of the block is 0.36 m above the lowest part of the slide and the s..
A 4.5 box slides down a 4.7 high frictionless hill, starting from rest, across a 1.6- -wide horizontal surface, afterwards hits a horizontal spring with spring constant 550 . The other end of the spring is anchored against a wall. The ground under..
A ray of light is incident on the surface of a block of clear ice at an angle of 33.0° with the normal. Find the angle between the reflected and refracted light
What is the magnitude of the electric field 19.7 cm directly above an isolated 3.25×10^?5 C charge? What is the direction of the electric field? Downward or upward?
A pair of slits, separated by 0.180 mm, is illuminated by light having a wavelength of ? = 612 nm. Express this path difference in terms of the wavelength
What horizontal force P must a worker exert on the rope to position 50 kg. crate directed over the trailer.
A molecule of DNA (deoxyribonucleic acid) is 2.05 µm long. The ends of the molecule become singly ionized: negative on one end, positive on the other. The helical molecule acts like a spring and compresses 0.88% upon becoming charged. Determine th..
A gymnast does a one handed handstand. The humerus, which isthe upper arm bone between the elbow and the shoulder joint, What is the compressional strain of the humerus
A small body of mass 0.13 kg is undergoing simple harmonic motion of amplitude 9.0 cm and period 0.10 s. What is the maximum value of the force acting on it? If the oscillations are produced by a spring, what is the spring constant?
A 2.03 kg book is placed on a flat desk. Suppose the coefficient of static friction between the book and the desk is 0.502, How much force is needed to keep the book moving at constant speed once it begins moving
Two forces, F? 1 and F? 2, act at a point. F? 1 has a magnitude of 8.20N and is directed at an angle of 62.0?, below the negative xaxis in the third quadrant What is the x component of the resultant force
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