🔑:In Federalist 78, Alexander Hamilton argued that the judiciary would be the weakest branch of the federal government, possessing "neither Force nor Will, but merely judgment." He believed that the judiciary's lack of control over the purse or sword would render it subservient to the other branches. However, as we reflect on the history of the Supreme Court, it becomes clear that Hamilton's assertion has proven largely incorrect. The judiciary has evolved into a powerful and influential institution, often shaping the course of American politics and society.One of the primary factors contributing to the judiciary's increased power is the doctrine of judicial review, which was established in the landmark case of Marbury v. Madison (1803). In this case, the Supreme Court, led by Chief Justice John Marshall, asserted its authority to declare laws unconstitutional, thereby establishing the Court as a co-equal branch of government. This decision marked a significant departure from Hamilton's vision of a weak judiciary, as it gave the Court a powerful tool to check the other branches and shape the constitutional landscape.The Court's exercise of judicial review has had far-reaching consequences, as seen in cases such as Brown v. Board of Education (1954) and Roe v. Wade (1973). In Brown, the Court struck down segregation in public schools, effectively overturning the "separate but equal" doctrine that had been in place since Plessy v. Ferguson (1896). This decision marked a major milestone in the Civil Rights Movement and demonstrated the Court's ability to drive social change. Similarly, in Roe, the Court established a woman's right to abortion, sparking a contentious national debate that continues to this day. These cases illustrate the Court's willingness to tackle complex and divisive issues, often taking a leading role in shaping American society and politics.Another factor contributing to the judiciary's increased power is the expansion of federal jurisdiction and the growth of the federal judiciary. The Judiciary Act of 1869 and the Judiciary Act of 1925, for example, increased the number of federal judges and expanded the Court's appellate jurisdiction. This expansion has enabled the Court to hear a wider range of cases, further solidifying its position as a national institution. Additionally, the Court's ability to review state and federal laws has given it significant influence over the development of American law, allowing it to shape the nation's legal landscape in profound ways.The Court's history is also marked by periods of activism and restraint, with different justices and judicial philosophies shaping the Court's approach to decision-making. The Warren Court (1953-1969), for example, was known for its liberal activism, issuing landmark decisions on issues such as civil rights, free speech, and reproductive rights. In contrast, the Rehnquist Court (1986-2005) and the Roberts Court (2005-present) have been characterized by a more conservative approach, with a focus on limiting federal power and promoting states' rights. These shifts in judicial philosophy have further underscored the Court's influence over American politics and society.In conclusion, Hamilton's assertion that the judiciary would be the weakest branch of government has proven largely incorrect. The doctrine of judicial review, the expansion of federal jurisdiction, and the growth of the federal judiciary have all contributed to the Court's increased power and influence. Through its decisions, the Court has shaped American society and politics, often taking a leading role in driving social change and resolving contentious national debates. As the Court continues to evolve and adapt to the changing needs of American society, it is clear that Hamilton's vision of a weak judiciary is no longer tenable. Instead, the judiciary has emerged as a co-equal branch of government, wielding significant influence over the course of American history.

🔑:## Step 1: Define the problem and the forces acting on the particleThe particle is under the sole influence of gravity, and we are tasked with finding its speed upon impact with the planet's surface. The gravitational force is given by (F = -frac{GMm}{r^2}), where (G) is the gravitational constant, (M) is the mass of the planet, (m) is the mass of the particle, and (r) is the distance from the center of the planet to the particle.## Step 2: Apply the conservation of energy principleThe conservation of energy principle states that the total energy of an isolated system remains constant. For our system, the total energy (E) is the sum of kinetic energy (K) and potential energy (U). The kinetic energy is given by (K = frac{1}{2}mv^2), where (v) is the velocity of the particle, and the gravitational potential energy is (U = -frac{GMm}{r}).## Step 3: Set up the initial and final conditionsInitially, the particle is at rest at a distance (r_0) from the planet's center, so its initial velocity (v_0 = 0). The initial energy (E_0) is thus purely potential: (E_0 = -frac{GMm}{r_0}). When the particle hits the planet's surface, it is at a distance (R) from the planet's center, and we want to find its velocity (v) at this point.## Step 4: Apply conservation of energyThe total energy at the start equals the total energy at the end: (E_0 = E). Substituting the expressions for (E_0) and (E), we get (-frac{GMm}{r_0} = frac{1}{2}mv^2 - frac{GMm}{R}).## Step 5: Solve for the final velocityRearranging the equation to solve for (v^2), we get (frac{1}{2}mv^2 = -frac{GMm}{r_0} + frac{GMm}{R}). Simplifying, (v^2 = 2GM(frac{1}{R} - frac{1}{r_0})). Since (r_0 >> R), (frac{1}{r_0}) is negligible compared to (frac{1}{R}), so (v^2 approx 2GM(frac{1}{R})). Taking the square root, (v approx sqrt{frac{2GM}{R}}).## Step 6: Recognize the expression for the final velocityThe expression (v = sqrt{frac{2GM}{R}}) is the same as the escape velocity from the surface of a planet, which makes sense because an object falling from a great distance will have a velocity equal to the escape velocity when it reaches the surface.The final answer is: boxed{sqrt{frac{2GM}{R}}}

🔑:The Mosaic Law Covenant, also known as the Sinai Covenant, is a pivotal event in the Old Testament that plays a crucial role in the history of Israel and the development of God's plan of salvation. This covenant was made between God and the nation of Israel at Mount Sinai, approximately 1,400 years before the birth of Christ. The Mosaic Law Covenant is significant because it:1. Established a unique relationship between God and Israel: The covenant created a special bond between God and the Israelites, making them His chosen people (Exodus 19:5-6). This relationship was based on mutual obligations, with God promising to be their God and they agreeing to obey His laws.2. Provided a code of conduct: The Mosaic Law Covenant included a comprehensive set of laws, known as the Torah, which governed various aspects of Israelite life, including worship, morality, and social justice (Exodus 20-23, Leviticus 1-27). These laws were designed to help the Israelites live in harmony with God and with each other.3. Defined Israel's role in the world: The covenant emphasized Israel's responsibility to be a light to the nations, demonstrating God's character and plan of salvation to the world (Isaiah 42:6, 49:6). Israel's obedience to the covenant would serve as a witness to the surrounding nations, showcasing the benefits of following God's laws.Terms and Conditions of the Mosaic Law CovenantThe Mosaic Law Covenant had several key terms and conditions:1. Obedience to the law: Israel was required to obey the laws and commandments given by God, which included the Ten Commandments (Exodus 20:1-17) and the various laws and regulations outlined in the Torah.2. Worship and sacrifice: The Israelites were instructed to worship God exclusively, offering sacrifices and observing various festivals and rituals (Leviticus 1-7, 23).3. Separation from the nations: Israel was commanded to maintain their distinctiveness from the surrounding nations, avoiding idolatry and intermarriage (Exodus 34:15-17, Deuteronomy 7:1-6).4. Consequences for disobedience: The covenant included warnings of punishment and judgment for disobedience, including exile and dispersion (Leviticus 26:14-39, Deuteronomy 28:15-68).Relationship to the Abrahamic CovenantThe Mosaic Law Covenant is closely related to the Abrahamic Covenant, which was made between God and Abraham approximately 430 years earlier (Genesis 12:1-3, 15:1-21). The Abrahamic Covenant promised:1. A land and a people: God promised to give Abraham a land and a numerous descendants, who would become a great nation (Genesis 12:2, 15:5).2. A blessing to the nations: Abraham's descendants would be a blessing to all nations, and through them, God would bring salvation to the world (Genesis 12:3, 22:18).The Mosaic Law Covenant built upon the Abrahamic Covenant, providing a framework for the Israelites to live in the Promised Land and fulfill their role as a light to the nations. The Mosaic Law Covenant also introduced a new aspect: the concept of a covenantal relationship between God and Israel, with mutual obligations and consequences.Implications for the Nation of Israel and the WorldThe Mosaic Law Covenant had significant implications for the nation of Israel and the world:1. Israel's history and identity: The covenant shaped Israel's history, culture, and identity, influencing their relationships with God, each other, and the surrounding nations.2. The concept of sin and guilt: The Mosaic Law Covenant introduced the concept of sin and guilt, highlighting the need for atonement and forgiveness (Leviticus 4-5, 16).3. The promise of a Messiah: The covenant hinted at the coming of a Messiah, who would redeem Israel and bring salvation to the world (Genesis 3:15, 49:10, Numbers 24:17).4. The universal scope of God's plan: The Mosaic Law Covenant demonstrated God's concern for all nations, not just Israel, and foreshadowed the universal scope of His plan of salvation (Isaiah 2:2-4, 11:10, 42:6).Relationship to the New TestamentThe Mosaic Law Covenant is closely related to the New Testament, as it:1. Fulfills the Abrahamic Covenant: The New Testament reveals that Jesus Christ is the fulfillment of the Abrahamic Covenant, bringing salvation to all nations (Galatians 3:6-9, 16).2. Supersedes the Mosaic Law Covenant: The New Testament teaches that the Mosaic Law Covenant has been superseded by the New Covenant, which is based on faith in Jesus Christ (Hebrews 8:6-13, 10:1-18).3. Provides a new way of relating to God: The New Testament introduces a new way of relating to God, based on faith, love, and the indwelling of the Holy Spirit, rather than obedience to the Mosaic Law (Romans 3:21-31, 8:1-11, Galatians 3:1-5).4. Unites Jews and Gentiles: The New Testament emphasizes that Jesus Christ has broken down the barrier between Jews and Gentiles, creating a new people of God, the Church, which includes believers from all nations (Ephesians 2:11-22, 3:6).In conclusion, the Mosaic Law Covenant is a pivotal event in the Old Testament that established a unique relationship between God and Israel, provided a code of conduct, and defined Israel's role in the world. The covenant is closely related to the Abrahamic Covenant and the New Testament, which fulfill and supersede it, respectively. The Mosaic Law Covenant has significant implications for the nation of Israel and the world, highlighting the need for atonement, the promise of a Messiah, and the universal scope of God's plan of salvation.

🔑:## Step 1: Determine the force on charge QThe force on charge Q can be determined by considering the electric field at large distance r from the center of the sphere. Since the total charge on the conductor S is zero, the electric field at large distances will be due to the charges q1 and q2. However, because the charges q1 and q2 are enclosed within the conductor and are not at its surface, they do not contribute to the external electric field according to Gauss's law and the concept of electrostatic shielding. Thus, the force on Q is due to the induced charges on the surface of the sphere, which would be zero if Q were the only external charge. However, since q1 and q2 are inside and the sphere's total charge is zero, the force on Q due to the sphere itself is zero when considering the sphere as a whole. The force on Q due to q1 and q2 directly is not shielded but is negligible at large distances compared to the force due to the sphere's induced charge, which is what we consider for external forces. Thus, the primary force on Q is due to the other charges (q1 and q2) but is more accurately described by the field they induce on the sphere, which at large distances, simplifies due to the sphere's charge distribution.## Step 2: Determine the force on the conductor SThe force on the conductor S as a whole is zero because the total charge on it is zero, and there are no external forces acting on it from other charges at a distance (since the force due to Q is considered in the context of Q's force, not as an external force acting on S). The internal forces due to q1 and q2 are balanced within the conductor.## Step 3: Determine the force on q1The force on q1 is due to q2 and the charge induced on the inner surface of the cavity containing q1. However, since the problem asks for forces at large distances from the sphere and not the detailed interaction within the sphere, we simplify by noting that the primary external force consideration for q1 is its interaction with q2 and the sphere's response. The force due to Q at large distance r is negligible compared to the forces within the sphere.## Step 4: Determine the force on q2Similar to q1, the force on q2 is due to q1 and the charge induced on the inner surface of the cavity containing q2. Again, the primary consideration for external forces is the interaction with q1 and the sphere's response, with the force due to Q being negligible at large distances.## Step 5: Consideration of approximation and dependence on rThe forces on Q, q1, and q2 due to each other and the sphere are approximate and depend on r being relatively large when considering the external influence of Q. For the sphere itself, the total force is exactly zero due to its zero net charge and the principle of superposition of forces.The final answer is: boxed{0}