The determinant is calculated as \( 1*4 - 2*3 = 4 - 6 = -2 \).

The determinant is calculated as \( 1*5 - 2*3 = 5 - 6 = -1 \).

The determinant is calculated as (3*4) - (2*1) = 12 - 2 = 10.

The determinant is calculated as \( 5*8 - 6*7 = 40 - 42 = -2 \).

Calculating gives a determinant of -3.

The dimension of electric charge is [M^1 L^2 T^-3 I^1].

Frequency is defined as the number of cycles per unit time, thus its dimension is [M^0L^0T^-1].

The gravitational constant G has dimensions of [M^-1L^3T^-2] as it relates mass, distance, and time in the law of gravitation.

The dimensional formula for acceleration is [M^0 L^1 T^-2], as it is defined as the change in velocity per unit time.

The dimensional formula for electric charge is [M^1 L^2 T^-3 I^-1], derived from the definition of current (I = Q/t).

Energy has the dimensional formula [M^1 L^2 T^-2], as it is measured in Joules (1 J = 1 kg·m²/s²).

The dimensional formula for frequency is [M^0 L^0 T^-1], as it is defined as the number of cycles per unit time.

Pressure is defined as force per unit area. The dimensional formula for force is M¹L¹T⁻², and for area is L², thus pressure = M¹L¹T⁻² / L² = M¹L⁻¹T⁻².

Velocity is defined as displacement per unit time, which gives the dimensional formula of [MLT⁻¹].

Work has the dimensional formula [M^1 L^2 T^-2].

The electric field due to a negative charge points towards the charge.

The electric field due to a positive charge points away from the charge.

The electric field lines point away from a positive charge.

According to Lenz's law, the induced current will flow in a direction that opposes the change, which is counterclockwise if the magnet is moved towards the coil.

According to Lenz's law, the induced current will flow in a direction that opposes the change in magnetic flux. If the magnetic field is increasing, the induced current will flow counterclockwise.

According to Lenz's law, the induced current will flow in a direction that opposes the change, so it will be counterclockwise if the magnetic field decreases.

According to the right-hand rule, if you point your thumb in the direction of the current, your fingers curl in the direction of the magnetic field lines, which is counterclockwise.

The direction of the magnetic field around a current-carrying wire is determined by the right-hand rule, which gives a clockwise or counterclockwise direction based on the current's direction.

Using the right-hand rule, if you point your thumb in the direction of the current, your fingers curl in the direction of the magnetic field, which is counterclockwise.

The direction of the magnetic field around a straight current-carrying conductor can be determined using the right-hand rule, which indicates that the field lines form concentric circles around the conductor in a counterclockwise direction when viewed from the positive end.

Using the right-hand rule, the magnetic field at the center of the loop is out of the plane.

According to the right-hand rule, the magnetic field lines around a straight conductor carrying current are circular and lie in planes perpendicular to the conductor.

Using the right-hand rule, the thumb points in the direction of current, and the fingers curl in the direction of the magnetic field.

The magnetic field produced by a current-carrying loop at its center is perpendicular to the plane of the loop, following the right-hand rule.

Using the right-hand rule, the magnetic field direction is counterclockwise around the wire.