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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?
A spring of constant 3.00 x 10^4 N/m is between a rigid beam and the output piston of a hydraulic lever. An empty container with negligible mass sits on the input piston. The input piston has Areai and output piston has area 18 A.
A battery having an emf of 11.10 V delivers 102 mA when connected to a 61.0 load. Find out the internal resistance of the battery.
Calculate the mass of the sun from the radius of the earth's orbit (1.50×1011 m), the earth's period in its orbit, and the gravitational constant G, What is the density of the sun
Disk 1 has a radius of 5 cm and mass of 1 kg it spins at an angular velocity of 2 rad/s a second disk is dropped on top of disk 1. what was the mass of the second disk
A sphere of mass 3.00 g is suspended from a cord. A steady horizontal breeze pushes the sphere so that the cord makes a constant angle of 28.0° with the vertical. Determine the tension in the cord
The mass of the barge is 9000 kg, and its acceleration is 0.15 m/s2 down the canal. Illustrate what are the magnitude and the direction of the force on the barge from the water?
A woman slowly lifts a box weighing 48.0 N from the floor to a shelf 1.50 m above, Find the net work done on the box
A - 5.00 nC point charge is on the x axis at x = 1.20 m . A second point charge Q is on the x axis at -0.600m. a) What must be the sign and magnitude of Q for the resultant electric field at the origin to be 45.0N/C in the + x direction?
Water flowing through a hose at 4.0 m/s fills a 800L child's wading pool in 7.0min. What is the diameter in cm of the hose
The ends of two thin glass tubes are stuck in the same pool of water. Although both tubes are thin, one tube has a smaller inside diameter (Tube 1) than the other (Tube 2). Both tubes are made of the same material. Would you expect the level in Tu..
The train comes to a stop 6m from the point at which it was released. What is the magnitude of train's acceleration after its wheel begins to stick.
An electron enters a region of space containing a uniform 0.0000179-T magnetic field. Its speed is 151 m/s, Find the radius r of the electron\'s path
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