prompt list | ground_truth string |
|---|---|
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2 seconds |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | moles HF: 0.10 mol
moles NaF: 0.10 mol
moles KF: 0.20 mol
[HF]: 0.095 M
[NaF]: 0.095 M
[KF]: 0.19 M |
[
{
"content": "Let \\( f: (0,1] \\to \\mathbb{R} \\) be a continuous function such that the improper integral \\( \\int_0^1 f(x) \\, dx \\) converges. Determine whether the following statement is true: \\( \\lim_{\\eta \\searrow 0} \\int_0^\\eta f(x) \\, dx = 0. \\) Justify your answer.",
"role": "user"
}
... | True |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.18 L/s |
[
{
"content": "Find the limit of the sequence \\( a_n = \\frac{7^n + 6^n - n^{100}}{(7.1)^n - 7^n + n^{101}} \\) as \\( n \\to \\infty \\).",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.671 x 10^-3 m^3 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.03 mV |
[
{
"content": "Find a solution to the differential equation \\( ty'' - (t+1)y' + y = 0 \\) that is not a constant multiple of the solution \\( y(t) = e^t \\).",
"role": "user"
}
] | t + 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.13e+04 W |
[
{
"content": "If $a$ and $b$ are integers such that for every prime $p$, there exists an integer $n_p$ satisfying $b \\equiv a^{n_p} \\pmod{p}$, can we conclude that there exists an integer $n$ such that $b = a^n$?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the integral \\( \\int_0^\\pi \\int_0^\\pi |\\cos(x+y)| \\, dx \\, dy \\).",
"role": "user"
}
] | 2\pi |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.89e+04 W |
[
{
"content": "Let $T_1$ be a random variable with probability density function (pdf) given by \\( f(t) = \\frac{6+2t}{7} \\), and let \\( T_2 \\sim \\text{Exp}\\left(\\frac{1}{3}\\right) \\). Given that $T_1$ and $T_2$ are independent, calculate \\( P(T_1 + T_2 > 1) \\).",
"role": "user"
}
] | \dfrac{6}{7} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $6,282.93 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 6.11 sec |
[
{
"content": "Determine all polynomials \\(P(x)\\) with real coefficients such that there exists a positive integer \\(n\\) for which the equation \\[P(x + \\frac{1}{n}) + P(x - \\frac{1}{n}) = 2P(x)\\] holds for all \\(x\\).",
"role": "user"
}
] | P(x) = ax + b |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.0059 M |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $13,000 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 75.075 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 28 m/s |
[
{
"content": "Evaluate the line integral \\(\\int_C \\vec G \\cdot \\vec{dr}\\) where \\(\\vec G(x,y,z) = (8xz + 5y)\\vec i + (2yz + 5x)\\vec j + (x^2 + 3z^2)\\vec k\\) and \\(C\\) is the curve consisting of the line segment from \\((1,0,1)\\) to \\((3,2,0)\\) followed by the parabola \\(y=x^2, z=1\\) from \\((... | -\dfrac{638}{3} |
[
{
"content": "On a square board with a side length of 2017, a chess bishop is placed in the lower-left corner. Alexey and Danil take turns moving the bishop, with Alexey moving first. The bishop can move diagonally any distance, but it cannot revisit any cell. The player who cannot make a move loses. Determine ... | Danil |
[
{
"content": "Let $F/K$ be a finite field extension and $p(x) \\in K[x]$ be an irreducible polynomial with a root in $F$. Does this imply that the degree of the extension $[F:K]$ is a multiple of the degree of $p(x)$?",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.7029 kg/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | behavior genetics |
[
{
"content": "Given that \\( a \\) and \\( b \\) are two orthogonal unit vectors, and \\( c \\cdot a = c \\cdot b = 1 \\), find the minimum value of \\( \\left|c + t a + \\frac{1}{t} b\\right| \\) for any positive real number \\( t \\).",
"role": "user"
}
] | 2\sqrt{2} |
[
{
"content": "Determine whether the limit of the function \\( F(x,y) = \\frac{x^{3} + y^{3}}{x^{2} + y^{2}} \\) exists as \\((x, y)\\) approaches the origin.",
"role": "user"
}
] | 0 |
[
{
"content": "Calculate the variance of a Laplace distribution with median 0 and scale parameter \\( \\alpha \\) using its characteristic function.",
"role": "user"
}
] | 2\alpha^2 |
[
{
"content": "Given the differential equation \\(y'(x, y_0) = y^2(x, y_0) + y(x, y_0) \\sin(x)\\) where \\(y_0\\) is the initial condition at \\(x=0\\), find the partial derivative \\(\\frac{\\partial y}{\\partial y_0}\\) evaluated at \\(y_0=0\\), i.e., \\(\\frac{\\partial y}{\\partial y_0}\\bigg|_{y_0=0}\\).",... | e^{1 - \cos x} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Chromium (Cr) |
[
{
"content": "Is it always possible to draw the edges of a planar graph without crossings, given arbitrary vertex positions in the plane?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the expression \\( n^{\\aleph_0} \\) for \\( n \\in \\mathbb{N} \\) and determine if it can be expressed as \\( \\aleph_1 \\).",
"role": "user"
}
] | \aleph_1 |
[
{
"content": "Evaluate the integral: $$\\int_{-\\infty}^\\infty \\frac{\\cos(x)}{x+i}\\,dx.$$",
"role": "user"
}
] | -\pi i e^{-1} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1,493,712 |
[
{
"content": "Evaluate the limit: $$\\lim\\limits_{(x,y)\\to(0,0)}\\frac{e^{x^2+y^2}-x^2-y^2-1}{(x^2+y^2)^2}$$",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Determine the least upper bound of the set \\(A=\\left\\{\\frac{1}{n}-\\frac{1}{m}:n,m\\in\\Bbb{N}\\right\\}.\\)",
"role": "user"
}
] | 1 |
[
{
"content": "In a building with 120 apartments and 119 residents, an apartment is considered overcrowded if it has at least 15 residents. Each day, the residents of one overcrowded apartment argue and move to different apartments. Will this process of moving eventually stop?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine if there exists a formal power series $S(x)$ such that $[S(x)]^2 = 2x + 2$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9,433,962.26 |
[
{
"content": "Find the general solution for the functional equation \\( g(x+y) = g(x) + g(y) \\), given that \\( g \\) is a continuous function.",
"role": "user"
}
] | g(x) = kx |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9.35% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.79 |
[
{
"content": "Find the coefficient of \\(x^6\\) in the expansion of \\((1-2x+3x^2-4x^3+5x^4)^4\\).",
"role": "user"
}
] | 1544 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 339V |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.9t^2 + 12t - 1.8 = 0 |
[
{
"content": "Determine the value of $p$ for which the following system of equations has a unique solution:\n\\[\\begin{align*}\na_1: & \\quad x + py + pz = p, \\\\\na_2: & \\quad x + p^2y = p^3, \\\\\na_3: & \\quad x + p^2y + pz = p, \\\\\na_4: & \\quad x + py + 2pz = p.\n\\end{align*}\\]",
"role": "user"
... | -1 |
[
{
"content": "Evaluate the integral \\( \\int_{\\mathbb{R}} x \\, d\\mu(x) \\) where the measure \\( \\mu = (1-p)\\delta_0 + p\\delta_1 \\) is defined on the Borel sets of \\( \\mathbb{R} \\). Here, \\( \\delta_x(B) = 1 \\) if \\( x \\in B \\) and \\( 0 \\) otherwise, for a Borel set \\( B \\).",
"role": "u... | p |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.55 knots, 23.69 degrees south of east |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.43 m/s |
[
{
"content": "Let $X$ be a random variable following a Poisson distribution with parameter $\\lambda = 1$. Derive the expected value of $3^X$, and show that $E(3^X) = e^2$. Provide a detailed explanation of your derivation.",
"role": "user"
}
] | e^2 |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to0}\\left|\\frac{\\Gamma(x)}{\\Gamma(-x)}\\right|$$",
"role": "user"
}
] | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.1 C |
[
{
"content": "The equation of the line shown can be written as $y=mx+b$. Find $mb$.\n[asy]\nsize(100,0);\nadd(shift(-5,-5)*grid(10,10));\ndraw((-5,0)--(5,0),linewidth(2));\ndraw((0,-5)--(0,5),linewidth(2));\nlabel(\"\",(5,0),E);\nlabel(\"\",(0,5),N);\ndraw((-3,-5) -- (2,5),blue,Arrows);\n[/asy]\nEach grid squa... | 2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9.35 g NH4Cl |
[
{
"content": "Let $S$ be the set of 81 points $(x, y)$ such that $x$ and $y$ are integers from $-4$ through $4$. Let $A$, $B$, and $C$ be random points chosen independently from $S$, with each of the 81 points being equally likely. The points $A$, $B$, and $C$ do not have to be different. Let $K$ be the area of... | \dfrac{200}{3} |
[
{
"content": "Is the language $B = \\{a^n b^n c^n \\}$ Turing recognizable? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Is it true that for a function $f$ in the disk algebra $A$, the spectrum $\\sigma_A(f)$ is equal to $f(D)$, where $D$ is the unit disk? Answer yes or no.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $1,379,000 |
[
{
"content": "Find the limit of the function \\( f(x,y) = \\frac{\\sin^2(xy)}{3x^2+2y^2} \\) as \\((x,y) \\to (0,0)\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Given the double summation \\( \\sum_{i=1}^{n}\\sum_{j=i}^{i+1}(3i+j) \\), change it to the form \\( \\sum_{j}^{}\\sum_{i}^{}(3i+j) \\) and calculate the result.",
"role": "user"
}
] | 4n^2 + 5n |
[
{
"content": "If a function $f$ is continuous on a real interval except for a single point where it is discontinuous, can $f$ be differentiable at that point?",
"role": "user"
}
] | No |
[
{
"content": "A coffee express machine has the following probabilities for each request: it brews coffee with probability \\( p_c = 0.9 \\), pours hot water with probability \\( p_w = 0.09 \\), and gets out of order with probability \\( p_f = 0.01 \\). Let \\( X \\) denote the number of coffees the machine prep... | 90 |
[
{
"content": "Solve for $n$: $2^n\\cdot 4^n=64^{n-36}$.",
"role": "user"
}
] | 72 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.81, 0.64, 0.49, 0.36, 0.25, 0.16 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 69.15 degrees |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.897 N |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to\\infty} (2x+1)^{x-\\sqrt{x^2-2}}$$ Is the limit equal to $1$ or $e^2$?",
"role": "user"
}
] | 1 |
[
{
"content": "Let $\\alpha \\neq 1$ be a complex number such that the distance from $\\alpha^2$ to 1 is twice the distance from $\\alpha$ to 1, while the distance from $\\alpha^4$ to 1 is four times the distance from $\\alpha$ to 1. Enter all possible values of $\\alpha,$ separated by commas.",
"role": "us... | i \sqrt{3}, -i \sqrt{3} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.046 mol |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | v_{1f} = (\frac{m_1-m_2}{m_1+m_2})v_{1i}+(\frac{2m_2}{m_1+m_2})v_{2i}, v_{2f} = (\frac{2m_1}{m_1+m_2}) v_{1i} + (\frac{m_2-m_1}{m_1+m_2}) v_{2i} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.042857 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Date|Interest Payment|Interest Expense|Amortization|Present Value
---|---|---|---|---
Jan. 1, 2017|-|-|-|2,273,375
Dec. 31, 2017|245,000|280,325|35,325|2,308,700
Dec. 31, 2018|245,000|280,325|35,325|2,334,025
Dec. 31, 2019|245,000|280,325|35,325|2,379,350
Dec. 31, 2020|245,000|280,325|35,325|2,414,675
Dec. 31, 2021|245... |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 7.79e-6 m^2 |
[
{
"content": "Determine whether the converse of the following statement is true: In an exact sequence $A \\rightarrow B \\rightarrow C \\rightarrow D \\rightarrow E$, if the map $A \\rightarrow B$ is surjective and $D \\rightarrow E$ is injective, then $C = 0$. Is the converse true?",
"role": "user"
}
] | Yes |
[
{
"content": "Find the minimum value of the expression \\(x^{\\ln(y)-\\ln(z)}+y^{\\ln(z)-\\ln(x)}+z^{\\ln(x)-\\ln(y)}\\) given that \\(x, y, z > 0\\).",
"role": "user"
}
] | 3 |
[
{
"content": "Given the polynomial function $f(x)$ that satisfies the equation $f(x)f(y) = f(x) + f(y) + f(xy) - 2$ for all real numbers $x$ and $y$, with $f(3) = 10$, find the value of $f(4)$. \\( \\boxed{} \\)",
"role": "user"
}
] | 17 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | [C]=2.9254*10^-3 M, [D]=[E]=0.4746*10^-3 M |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 6.4 m/s |
[
{
"content": "Find the solutions to the functional differential equation \\( f'(x) - f(\\alpha x) = 0 \\), given that \\( f(0) = 0 \\), \\( f: \\mathbb{R}^+ \\rightarrow \\mathbb{R} \\), and \\( 0 < \\alpha < 1 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1. Production opportunities
2. Time preferences for consumption
3. Risk
4. Inflation |
[
{
"content": "Consider the function \\( f(x,y) = ax + by \\), where \\((a,b) \\neq (0,0)\\), defined on a closed and bounded set \\( \\mathcal{D} \\). If \\( \\mathcal{D} \\) is a polygon, does the function \\( f \\) attain its extremum points on the vertices of \\( \\mathcal{D} \\) even if \\( \\mathcal{D} \\)... | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Van De Graff generator |
[
{
"content": "Evaluate the limit \\( \\lim_{n \\to \\infty} \\left( \\frac{1^k + 2^k + \\cdots + n^k}{n^k} - \\frac{n}{k+1} \\right) \\) where \\( k \\in \\mathbb{N} \\).",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Given a function $f: \\mathbb{R}^2 \\to [0,1]$, if the limit $\\lim_{x\\to\\infty} \\lim_{y\\to\\infty} f(x,y)$ exists, determine whether we can conclude that for sufficiently large $x$, the limit $\\lim_{y\\to\\infty} f(x,y)$ also exists.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.1% |
[
{
"content": "Determine whether the existence of a unique solution for the equation \\(A\\mathbf{x} = \\mathbf{b}\\) for some vector \\(\\mathbf{b}\\) implies that the matrix \\(A\\) has a left inverse. Assume \\(A\\) is an \\(m \\times n\\) matrix.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the order of the center of the general linear group \\( GL_n(\\mathbb{C}) \\). Express your answer as \\( |Z(GL_n(\\mathbb{C}))| = \\boxed{?} \\).",
"role": "user"
}
] | \infty |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Firms should avoid ambiguous or incomplete contracts, engage in long-term contracts or close relationships with suppliers, and consider vertical integration (e.g., backward integration) to reduce dependence and control costs. |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 10049V |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 271.73 Pa |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $8,864 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 59 kg |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.607 N |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 17.4 m/s |
[
{
"content": "Calculate the limit \\( \\lim_{n\\to \\infty}\\left(\\dfrac{f\\left(a+\\frac{1}{n}\\right)}{f(a)}\\right)^{1/n} \\), given that the function \\( f:\\mathbb{R}\\to \\mathbb{R} \\) is differentiable at \\( a\\in \\mathbb{R} \\) and satisfies \\( f(a) > 0 \\).",
"role": "user"
}
] | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $41,377 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 25.57 m |
[
{
"content": "Calculate the flux of the vector field \\( F(x,y,z)=(x^2,y^2,z^2) \\) through the surface \\( S \\) defined by \\( x^2+y^2+z^2=4 \\), oriented with the outward-pointing normal vector.",
"role": "user"
}
] | 0 |
[
{
"content": "Given a sequence of continuous functions \\( \\{f_n\\} \\) that uniformly converges to \\( f(x)=0 \\) on the interval \\([1,\\infty)\\) and satisfies \\( \\int_{1}^{\\infty}f_{n}(x)\\,dx \\le 1 \\) for all \\( n \\ge 1 \\), determine whether \\( \\lim_{n\\to \\infty}\\int_{1}^{\\infty}f_{n}(x)\\,d... | False |
[
{
"content": "Determine all functions \\( f : \\mathbb{R} \\rightarrow \\mathbb{R} \\) that satisfy the following conditions for all \\( x, y \\in \\mathbb{R} \\):\n1. \\( |f(x)| = |x| \\)\n2. \\( f(f(-y)) = -f(y) \\)\n3. \\( f(f(x)) = f(x) \\)",
"role": "user"
}
] | f(x) = x |
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