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"What is the total work done on an object when it is moved upwards against gravity, considering both(...TRUNCATED) | ["<think>\nOkay, so I need to figure out the total work done on an object when it's moved upwards ag(...TRUNCATED) |
"Propose a system of 'Practical Numbers' that denies the Axiom of Choice and the notion of infinity.(...TRUNCATED) | ["<think>\nOkay, so I need to propose a system of 'Practical Numbers' that denies the Axiom of Choic(...TRUNCATED) |
"Solve the differential equation (1/F)(dF/dx) = 2, where F is a function of x and y. Use the method (...TRUNCATED) | ["<think>\nOkay, so I need to solve this differential equation: (1/F)(dF/dx) = 2. Hmm, let me think.(...TRUNCATED) |
"Two equal masses, each with a mass similar to that of the sun, are separated by a distance of 1 lig(...TRUNCATED) | ["<think>\nOkay, so I have this problem about two equal masses, each similar to the sun, separated b(...TRUNCATED) |
"Prove that for a vector space V = F^n, where n ≥ 1 and F is a field, there do not exist linear ma(...TRUNCATED) | ["<think>\nOkay, so I need to prove that there are no linear maps S and T from V = F^n to itself suc(...TRUNCATED) |
"Discuss the feasibility of solving the particle in a box problem in quantum mechanics using creatio(...TRUNCATED) | ["<think>\nOkay, so I need to discuss how to solve the particle in a box problem using creation and (...TRUNCATED) |
"Given the area of a parallelogram is 420 square centimeters and its height is 35 cm, find the corre(...TRUNCATED) | ["<think>\nOkay, so I need to find the base of a parallelogram when I know the area and the height. (...TRUNCATED) |
"What is the minimum number of red squares required to ensure that each of $n$ green axis-parallel s(...TRUNCATED) | ["<think>\nOkay, so I need to figure out the minimum number of red squares required to ensure that e(...TRUNCATED) |
"Two 3.0g bullets are fired with speeds of 40.0 m/s and 80.0 m/s respectively. What are their kineti(...TRUNCATED) | ["<think>\nOkay, so I need to figure out the kinetic energies of these two bullets and then compare (...TRUNCATED) |
"Consider a partial differential equation (PDE) of the form \\(u_t = ku_{xx}\\) with initial conditi(...TRUNCATED) | ["<think>\nOkay, so I have this partial differential equation (PDE) given by $u_t = k u_{xx}$ with i(...TRUNCATED) |
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