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    Net force between two identical dipoles

    You can find the fields, and use superposition on the fields, and then multiply by the charge. The field of a dipole and also that of the other charge, that is.
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    F''(x) Second Derivative problem

    Try taking the first derivative first, then take the second derivative.
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    Matrix exponential

    The actual sum would depend on element of the domain chosen where the image is to be evaluated.
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    Funny question

    The time allowed for acclerating is longer if the pad is hit than if something with a high elasticity is hit, then the force would be less because force is change in momentum relative to change in time. Are you all right?
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    Series question

    Exponents of the form n^n grows much faster than factorials of the form (n!) because the factorial is a multiplication of n terms, the majority of which are less than n, and the power is a multiplication of n terms, all of which are equal to n.
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    Matrix exponential

    Yes, sorry, I meant, in a series, not closed form, hahah, do you need the actual sum?
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    Need help setting up triple integral in spherical coordinates

    The boundaries are given by the limits to the integration. How did you arrive at the limits? No, they are not wrong, if the center of the sphere is at the point where all the cartesian coordinates are zero.
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    Divergence Problem

    Integrate over the surface using the transformation to cylindrical co-ordinates, using x = square_root(16) cos(theta) and similarly for y, and the divergence theorem gives support to your integrating over the vector field, once you have added in the jacobian, from zero to two pi for theta, and...
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    Matrix exponential

    Notice \begin{bmatrix}-1 & 2 & 0\\-2 & -1 & 0\\ 0 & 0 & -3\end{bmatrix} ^i = \begin{bmatrix}{((-1)^i (2i-1))} & {((-1)^{i-1} 2i)} & 0\\{(-1)^{i} 2i)} & {((-1)^i (2i-1))} & 0\\ 0 & 0 & (-3)^i\end{bmatrix}. The series then is easily represented in a closed form.
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    Voltage and current calculation on a mixed circuit

    It might be well to read up on "Delta-Wye" transformations.
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    Different dielectric material with different relative permittivity

    The voltage between the plates remains, unchanging, the capcitance is calculated by, C_{ca} = {\epsilon}_0 {\epsilon}_r \frac {A}{d}. This in fact happens in real life, when capacitors are heated and one of the two plates in a parallel plate capacitor pulls away from the dielectric, another...
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    Simple Temperature problem

    Try using the other equation you have, though I know not what it is, and then, \Delta V = (1-\frac{1}{8}) V_0, from which it seems that the original volume is not here required. -the final temperature is the change in temperature plus the original temperature
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    Very very quick quiestion about D_4?

    Forgive me, I am probably wrong, but I thought that the mapping from 1234 to the permutations that go along with the reflections and rotations described were the automorphisms, and the automorphisms formed the automorphism group of the dihedral group that we are talking about. In which case, the...
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    Underwater Lightbulb Optical Illusion - Reflection/Refraction of Light

    The refraction of light from water to a curved glass then to air might cause the glass of the light bulb to look thicker. An optically opaque coating has no index of refraction of meaning, and is not part of the explanation.
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    Very very quick quiestion about D_4?

    Consider a square, and label the vertices 1, and 2, and 3, and 4. Then, proceed to record the automorphisms as you rotate it and reflect it along its axes of symmetry. Then, you'll be able to find all eight automorphisms if you do not forget, as some might, though I trust you wouldn't, the...
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    Similarity is transitive

    If A = P B Pinv and B = K C Kinv, where Pinv is the inverse of P, and mutatis mutandis for K, use the property that (PK)inv is (Kinv)(Pinv). and hence A = (PK) C (PK)inv.
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    Door Torque Question - Solved Question

    The centre of mass of the door is at the point halfway between the two ends of the width of the door, and the width of the door is h/2 and half of that is \frac{h}{4}. There is a force applied in another orientation that also produces a moment about the same point.
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    AP Calculus

    The part letter b asks only for a direction, so the answer should either be positive or negative. In part letter d, you would do better to identify the roots of the displacement equation and find the displacements in each direction (the intervals separated by the zeroes), and then add the...
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    Newton's 2nd Law Problem

    When breaks are applied, the only forces on the car are gravitational forces and frictive forces, and of these only the frictive force acts in the horizontal direction in which the car is travelling. Hence the sum of forces in the x direction is F_{f}=\mu F_{n} , where mu is the co-efficient of...
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    Projectile Motion

    The motion in the horizontal direction is not accelerated in any way and hence the velocity in the horizontal direction is constant. Use the the components method then to express the initial velocity of the ball horizontally and vertically. Knowing the distances, use the kinematics equations to...
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    Acceleration due to gravity homework

    Use the expression for the gravitational force, then equate that force to ma, there being an m in your expression for the gravitational force, the "m"s would devide out.
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    Science, engineering or maths? >.<

    You could start out as an engineer in your undergraduate studies, then take a some other graduate degree. Then you can be both. Oh and did you know that the actor most known for playing the character "Mister Bean" actually studied electrical engineering? Really, what you study as an...
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    Complex Numbers

    Attempt to multiply the number by \frac{9-4i}{9-4i}. Then you can easily separate the real and imaginary parts.
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    Studying for calc?

    The length of a curve is given by ds^{2}=dx^{2}+dy^{2}, given by Pythagoras' Theorem. Dividing throughout by dx^{2}, we have ds= \sqrt{1+(\frac{dy}{dx})^2} . Integrating both sides, you can find the length, s, of the curve. Work is force integrated over distance. Imagine little disks of...
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    Find Acceleration

    Resolve the force vectors into their components and the use F=m \bullet a.
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    Force on box

    Yes, it does mean you have to apply another force parallel to the incline to have \sum F = 0 . Once the equilibrium position is reached the box moves with constant velocity, in this case it would be zero (i.e., at rest).
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    Calc II question help

    f'(x)= \frac{1}{f^{-1}'(x)}
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    Integral Xabs(x)

    You would still split it up and add the integral for x>0 up with the one for x<0.
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