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 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.

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.

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.

The direction of the magnetic field produced by a current-carrying wire is perpendicular to both the wire and the direction of the current.

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

The standard form of a parabola is (y - k)^2 = 4p(x - h). Here, p = 2, so the directrix is x = -2.

For the parabola y^2 = 4px, here 4p = 8, so p = 2. The directrix is x = -p = -2.

The distance between centers (1, 2) and (-3, -4) is calculated using the distance formula.

The distance between the foci is given by 2c, where c = √(a^2 - b^2) = √(25 - 16) = 3, so the total distance is 2c = 6.

Distance = √[(4-1)² + (6-2)²] = √[9 + 16] = √25 = 5.

Distance = √[(7-3)² + (1-4)²] = √[16 + 9] = √25 = 5.

Distance = √((4-1)² + (5-2)² + (6-3)²) = √(9 + 9 + 9) = 3√3.

Distance = |3(1) + 4(2) - 10| / √(3² + 4²) = |3 + 8 - 10| / 5 = 1.

Distance = |2(3) + 3(4) - 6| / √(2² + 3²) = |6 + 12 - 6| / √13 = 12/√13.

The function is undefined at x = 2, so the domain is all real numbers except 2.

The function is undefined at x = 3, so the domain is x ≠ 3.

The expression under the square root must be non-negative, so x - 1 >= 0, hence x >= 1.

The Doppler effect refers to the change in frequency of a wave in relation to an observer moving relative to the wave source.

Dot product = 1*3 + 2*4 = 3 + 8 = 11

A . B = 2*1 + 3*0 + 4*(-1) = 2 + 0 - 4 = -2.

The eccentricity e of a hyperbola is given by e = √(1 + b^2/a^2).