A skew-symmetric matrix satisfies the condition a_ij = -a_ji for all i and j.

A symmetric matrix satisfies the condition Aij = Aji for all i and j.

A symmetric matrix is defined by the property A = A^T, meaning it is equal to its transpose.

A matrix A is symmetric if it is equal to its transpose, i.e., A = A^T.

Total calories = (40g * 4) + (10g * 4) + (5g * 9) = 160 + 40 + 45 = 245 calories.

Total calories = (50g * 4) + (20g * 4) + (10g * 9) = 200 + 80 + 90 = 370 calories.

A relative error of 5% indicates that the measurement is off by 5% of the true value.

Accuracy refers to how close a measurement is to the true value.

Accuracy refers to how close a measured value is to the true value.

The leading zeros are not significant. Therefore, 0.00456 has 3 significant figures.

Leading zeros are not significant. The significant figures are 4, 5, 6, which gives a total of 4 significant figures.

The measurement 0.00780 m has three significant figures (the zeros before the 7 are not significant, but the zero after the 8 is).

The leading zeros are not significant, but the trailing zero after 78 is significant. Therefore, it has 3 significant figures.

Leading zeros do not count as significant figures. The significant figures in 0.007890 are 7, 8, 9, and 0, which totals to 4 significant figures.

Absolute error = |Measured value - True value| = |12.30 - 12.5| = 0.2 cm.

The number 1500 m has 2 significant figures unless specified otherwise (e.g., with a decimal point). Without a decimal, trailing zeros are not counted.

Without a decimal point, trailing zeros are not considered significant. Therefore, 1500 has 2 significant figures.

A precision of 0.01 cm implies that the measurement can vary by this amount, indicating the level of uncertainty.

Total time range = 15.0 ± 0.5 = 14.5 s to 15.5 s.

The meeting starts at 10 AM and lasts for 2 hours, so it ends at 12 PM.

The meeting will end at 2:45 PM.

Total years served = 5 years + 5 years = 10 years.

Number of terms = 20 years / 5 years per term = 4 terms.

Members retiring every 2 years = 1/3 of 245 = 81.67, rounded down to 81. Therefore, 41 members can be elected every year.

If 245 members serve 6 years, then 245/6 = 40.83, approximately 41 members complete their term in a year.

Using the equation λ = hc/E, where E = 2 eV = 2 * 1.6 x 10^-19 J, we find the minimum wavelength λ = (6.63 x 10^-34 J·s * 3 x 10^8 m/s) / (2 * 1.6 x 10^-19 J) = 310 nm.

The threshold wavelength can be calculated using the equation λ = hc/W. Substituting h = 4.14 x 10^-15 eV·s, c = 3 x 10^8 m/s, and W = 2 eV gives λ = 620 nm.

The maximum kinetic energy can be calculated using KE = hf - φ. Here, KE = 5.0 eV - 2.0 eV = 3.0 eV.

Maximum wavelength (λ) = hc/Φ = (1240 nm·eV)/(3 eV) = 413.33 nm.

The minimum wavelength can be calculated using the equation λ = hc/W. Substituting h = 4.14 x 10^-15 eV·s, c = 3 x 10^8 m/s, and W = 4 eV gives λ = 310 nm.