An orthogonal matrix is defined as a matrix whose transpose is equal to its inverse.

A matrix is not invertible if its determinant is zero. The matrix [[0, 1], [0, 0]] has a determinant of 0.

A symmetric matrix is one that is equal to its transpose. Matrix B is symmetric because B = B^T.

Mean is a measure of central tendency, not dispersion.

Range is affected by extreme values as it is calculated as the difference between the maximum and minimum values.

Zinc is used as the anode in a Daniell cell.

Aluminum is commonly used as an anode in electrolysis due to its high reactivity.

Copper cannot be used as an anode in a galvanic cell because it is less reactive than zinc.

Gold has the highest standard reduction potential among the given metals.

Gold is highly resistant to corrosion, which is why it is often used in jewelry and electronics.

Gold is known to be the least reactive metal, making it resistant to corrosion and oxidation.

Gold is known to be the most malleable metal, capable of being drawn into extremely thin sheets.

Sodium reacts vigorously with water at room temperature, producing sodium hydroxide and hydrogen gas.

Mercury is the only metal that is liquid at room temperature.

Sodium is a highly reactive metal, especially with water, compared to the other metals listed.

Silver is the best conductor of electricity among metals due to its high electron mobility.

Aluminum is widely used in aircraft manufacturing because of its lightweight and strength.

Copper is widely used in electrical wiring due to its excellent conductivity.

Sodium reacts vigorously with water to produce sodium hydroxide and hydrogen gas.

Regular calibration of instruments can help reduce zero error by ensuring that the instrument reads zero accurately.

Vasectomy is a surgical procedure that provides a permanent form of contraception for males.

Filtration is a physical separation method and does not identify chemical groups, unlike the other methods listed.

Dialysis is used to purify colloidal solutions by allowing the solvent and small solutes to pass through a semi-permeable membrane while retaining the colloidal particles.

Electrophoresis is used to stabilize colloidal solutions by applying an electric field to separate charged particles.

All of the mentioned microbes can be involved in fermentation processes, but bacteria and fungi are the most common.

Lactobacillus is the primary bacterium used in the fermentation process to produce yogurt.

Fungi, particularly the genus Penicillium, are used in the production of antibiotics like penicillin.

Rhizobium is a bacterium that forms symbiotic relationships with legumes and is used in biofertilizers for nitrogen fixation.

Bacteria are commonly used in the production of biofuels through fermentation processes.

Genetically modified bacteria are used in the production of insulin for diabetes treatment.