What is the derivative with respect to x of the function f(x) = x³ · e^(2x)?
Matematica E Calculo Istm
Question · Medium
Every level, the water flows faster
Short
Evaluate the definite integral: ∫ (from 0 to 2) (3x² - 4x + 1) dx.
Question · Easy
What is the determinant of the 3×3 matrix A = [[1, 2, 3], [0, 4, 5], [0, 0, 6]]?
Solve the first-order separable differential equation dy/dx = 2x · y for y > 0 with initial condition y(0) = 3.
What is the modulus |z| and argument θ of the complex number z = 1 + i√3?
What is the equation of the ellipse centered at (0, 0) with major axis of length 10 along the x-axis and minor axis of length 6 along the y-axis?
Calculate the eigenvalues of the 2×2 matrix A = [[3, 1], [0, 2]].
Using L'Hôpital's rule, evaluate the limit: lim (x → 0) [ (e^(3x) - 1) / sin(2x) ].
What is the cross product u × v of vectors u = (1, 0, 0) and v = (0, 1, 0)?
What is the general solution of the second-order homogeneous differential equation y'' + 9y = 0?
What is the inverse of the 2×2 matrix A = [[2, 5], [1, 3]]?
What is the arc length of the parametric curve x(t) = 3cos(t), y(t) = 3sin(t) for 0 ≤ t ≤ π?
What is the Taylor series expansion of e^x about x = 0 (Maclaurin series)?
If vector field F(x, y, z) = (2xy, x² + z, y), what is the curl of F (∇ × F)?
Question · Hard
What is the Laplace transform of the function f(t) = sin(2t)?
In a DC electrical circuit, three resistors R₁ = 10 Ω, R₂ = 20 Ω, and R₃ = 20 Ω are connected such that R₂ and R₃ are in parallel, and this pair is in series with R₁. What is the equivalent resistance R_eq?
Fisica Geral E Eletrotecnica
According to Faraday's Law of Induction, what is the induced electromotive force (EMF / ε) in a coil of N turns through which magnetic flux Φ_B changes with time?
What is the maximum theoretical efficiency of a Carnot heat engine operating between a hot reservoir at T_H = 600 K and a cold reservoir at T_C = 300 K?
A structural steel rod of cross-sectional area A = 2 × 10⁻⁴ m² is subjected to a tensile axial force of 40,000 N. What is the normal stress σ in the rod?
What is the resonant frequency f₀ of an RLC series circuit with inductance L = 10 mH (0.01 H) and capacitance C = 10 µF (10⁻⁵ F)? (Use f₀ = 1 / (2π√(LC)))
In statics, what are the three equilibrium conditions for a 2D coplanar rigid body structure?
What is Hooke's Law relating tensile stress σ and strain ε within the elastic deformation limit of an engineering material?
What is the fundamental difference between an Otto cycle (spark-ignition) and a Diesel cycle (compression-ignition)?
A light wave in air (n₁ = 1.0) strikes an optical glass prism (n₂ = 1.5) at an incidence angle of 30°. Using Snell's Law (n₁·sin(θ₁) = n₂·sin(θ₂)), what is sin(θ₂) of the refracted ray?
What is the torque τ produced by a force F = (0, 50, 0) N applied at position r = (2, 0, 0) meters relative to the pivot point?
What is the molar mass of ammonium nitrate (NH₄NO₃), a chemical compound used in industrial explosives and propellants? (Atomic masses: N=14, H=1, O=16 g/mol)
Quimica Geral E Dos Materiais
What is the balanced stoichiometric chemical equation for the complete combustion of propane gas (C₃H₈)?
In electrochemistry, what is Galvanic Corrosion (corrosão galvânica) and when does it occur in military structures?
What is the primary difference between Deflagration (deflagração) and Detonation (detonação) in explosive chemistry?
Which metal is the primary alloying element added to iron (carbon steel) in amounts greater than 10.5% by mass to produce corrosion-resistant Stainless Steel (aço inoxidável)?
What is the primary institutional mission of the Instituto Superior Técnico Militar (ISTM) in Luanda?
Ciencias Militares E Engenharia Aplicada
In exterior ballistics, what is the primary cause of 'Deriva Giroscópica' (Spin Drift / Gyroscopic Drift) of a spinning artillery projectile?
What is the Radar Range Equation relating maximum radar detection range R_max to transmitted power P_t, antenna gain G, radar cross section σ, and minimum detectable signal S_min?
What is the primary professional ethical obligation of a military engineer graduated from ISTM when designing military structures, bridges, or fortifications?
What type of military bridge can be rapidly deployed by combat engineers using specialized armored vehicle chassis (AVLB / Lançador de Pontes Blindado) to cross anti-tank ditches and river obstacles?
In digital telecommunications, what is the Nyquist Sampling Theorem minimum sampling rate f_s required to perfectly reconstruct a bandlimited analog signal with maximum frequency f_max?
What is the principal chemical component and oxidizer used in solid rocket motor propellants for military missiles?
What is the principle of a Shaped Charge (Carga Oca / Efeito Munroe) in anti-tank warheads (HEAT)?
What is the function of an Operational Amplifier (Amp-Op / Op-Amp) in an inverting configuration with input resistor R_in = 10 kΩ and feedback resistor R_f = 100 kΩ?
In fluid mechanics, what does the Reynolds Number (Re = ρ · v · D / µ) indicate regarding fluid flow inside a pipe or conduit?
What is the pH of a 0.001 M (10⁻³ mol/L) hydrochloric acid (HCl) aqueous solution at 25°C?
What is the purpose of 'Cathodic Protection' (protecção catódica com ânodo de sacrifício) on naval ship hulls in the Marinha de Guerra Angolana?
In telecommunications, what is the bandwidth of an optical fiber transmission channel operating at carrier frequency f_c = 193 THz with a wavelength band of Δλ = 40 nm centered at λ = 1550 nm? (c = 3 × 10⁸ m/s; Δf ≈ c · Δλ / λ²)
What is the critical load P_cr for buckling of an ideal pinned-pinned structural column according to Euler's Column Formula?
In digital electronics and microprocessors, what is the output of a 2-input XOR logic gate when both inputs are equal to logical 1 (A = 1, B = 1)?
What is the primary function of a Three-Phase Induction Motor (motor de indução trifásico) in military and naval industrial installations?
What is the half-life of a radioactive isotope used in non-destructive gamma radiography testing of military tank armor welds?
Loading more…