The set of all mappings from N to N, where N represents the set {1, 2, 3, 4}, consists of all possible functions that assign each element in the domain set {1, 2, 3, 4} to an element in the codomain set {1, 2, 3, 4}. Each mapping represents a unique way of pairing elements from the domain to elements in the codomain. There are a total of 4^4 = 256 possible mappings from N to N in this case. **

To show that the mapping n x n -> n^m * 2^n+1 - 1 is a bijection, we need to demonstrate that it is both injective and surjective. To show injectivity, we need to prove that distinct elements in the domain map to distinct elements in the codomain. This can be done by showing that if (a, b) and (c, d) are distinct pairs in n x n, then n^m * 2^a+1 - 1 and n^m * 2^c+1 - 1 are distinct in n^m * 2^n+1 - 1. To show surjectivity, we need to prove that every element in the codomain has a pre-image in the domain. This can be done by showing that for every element in n^m * 2^n+1 - 1, there exists a pair (a, b) in n x n such that **

Hippies liked Rock 'n' Roll because it represented a form of rebellion against mainstream society and traditional values. The music's energetic and rebellious nature resonated with the countercultural movement of the 1960s and 1970s. Rock 'n' Roll also promoted freedom, self-expression, and individuality, which were important values for hippies who sought to break away from societal norms and embrace a more liberated lifestyle. Additionally, the music's themes of love, peace, and unity aligned with the hippie philosophy of promoting harmony and togetherness. **

Rock 'n' roll has proven to be a resilient and enduring genre that has evolved and adapted over the years. While its popularity may ebb and flow, it is unlikely to ever completely die out. Its influence can be seen in various other genres of music, and there will always be artists and fans who keep the spirit of rock 'n' roll alive. As long as there are people who are passionate about the music and its rebellious attitude, rock 'n' roll will continue to have a place in the music world. **

No, 1 kg is not equal to 1 N. The kilogram (kg) is a unit of mass, while the newton (N) is a unit of force. The relationship between the two is given by Newton's second law of motion, which states that force (in newtons) is equal to mass (in kilograms) multiplied by acceleration (in meters per second squared). Therefore, 1 kg is equal to 9.81 N on the surface of the Earth due to the acceleration due to gravity. **

Rock 'n' roll pictures often capture the energy and rawness of the music genre. They can feature dynamic and intense performances, close-up shots of musicians expressing themselves, and the passionate connection between the artists and their audience. The images may also convey a sense of rebellion, freedom, and the overall attitude associated with rock 'n' roll. The use of bold colors, dramatic lighting, and gritty textures can further enhance the visual impact of these pictures. **

The best rock 'n' roll song is subjective and can vary depending on personal taste. Some classic contenders for the title include "Johnny B. Goode" by Chuck Berry, "Stairway to Heaven" by Led Zeppelin, "Bohemian Rhapsody" by Queen, and "Born to Run" by Bruce Springsteen. Each of these songs has had a significant impact on the rock 'n' roll genre and has stood the test of time as iconic rock anthems. Ultimately, the best rock 'n' roll song is the one that resonates the most with each individual listener. **

The function is continuous and differentiable in the interval [n, 1/n] because it is a composition of continuous and differentiable functions. The function f(x) = 1/x is continuous and differentiable for all x ≠ 0, and the function g(x) = x is continuous and differentiable for all x. Since the composition of continuous functions is continuous, and the composition of differentiable functions is differentiable, the function h(x) = f(g(x)) = f(x) = 1/x is continuous and differentiable in the interval [n, 1/n]. **